{"id":4930,"date":"2024-10-05T21:01:01","date_gmt":"2024-10-05T13:01:01","guid":{"rendered":""},"modified":"2024-10-05T21:01:01","modified_gmt":"2024-10-05T13:01:01","slug":"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90","status":"publish","type":"post","link":"https:\/\/mushiming.com\/4930.html","title":{"rendered":"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90"},"content":{"rendered":"<p><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"display: none;\"> \n <path stroke-linecap=\"round\" d=\"M5,0 0,2.5 5,5z\" id=\"raphael-marker-block\" style=\"-webkit-tap-highlight-color: rgba(0, 0, 0, 0);\"><\/path> \n<\/svg> <\/p>\n<div class=\"toc\">\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u4e00\u3001Cycle GAN\uff08CGAN\uff09\u539f\u7406<\/li>\n<li>\n<ul>\n<li>1.1Conditional GAN<\/li>\n<li>1.2Unsupervised Conditional GAN<\/li>\n<li>\n<ul>\n<li>No.1 Direct Transformation\uff0c\u76f4\u63a5\u8f6c\u6362<\/li>\n<li>No.2 Projection to Common Spcae\uff0c\u5148\u7f16\u7801\u51fa\u62bd\u8c61\u7279\u5f81\uff0c\u5728\u89e3\u7801\u8f6c\u6362\u4e3a\u56fe\u50cf<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\u4e8c\u3001\u4ee3\u7801\u90e8\u5206<\/li>\n<li>\n<ul>\n<li>2.1\u8d85\u53c2\u6570<\/li>\n<li>2.2\u6570\u636e\u9884\u5904\u7406<\/li>\n<li>2.3\u7f51\u7edc<\/li>\n<li>2.4\u4f18\u5316\u5668\u548c\u635f\u5931\u51fd\u6570<\/li>\n<\/ul>\n<\/li>\n<li>\u4e09\u3001\u8fd0\u884c\u7ed3\u679c<\/li>\n<li>\n<ul>\n<li>3.1CUDA\u5360\u6ee1\u95ee\u9898<\/li>\n<li>3.2\u8bad\u7ec3\u8fc7\u7a0b<\/li>\n<li>\n<ul>\n<li>\uff081\uff09Epoch:10<\/li>\n<li>\uff082\uff09Epoch:20<\/li>\n<li>\uff083\uff09Epoch:50<\/li>\n<li>\uff084\uff09Epoch:100<\/li>\n<li>\uff085\uff09Epoch:200<\/li>\n<li>\uff086\uff09\u6c47\u603b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\u56db\u3001\u5c0f\u7ed3<\/li>\n<li>\u4e94\u3001\u76f8\u5173\u4ee3\u7801\u53ca\u53c2\u8003\u8d44\u6599<\/li>\n<\/ul>\n<\/div>\n<h2>\u4e00\u3001Cycle GAN\uff08CGAN\uff09\u539f\u7406<\/h2>\n<p>\u2003\u2003CycleGAN\u6765\u81ea\u4e8euncongditional GAN\uff0c\u9996\u5148\u4ecb\u7ecd\u4e00\u4e0bconditional GAN\u548cunconditional GAN\u3002<\/p>\n<h3>1.1Conditional GAN<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/5547b7325fb9465c8e0c4f48667cf529.png\" =\"\" =\"\u56fe\u7247\u622a\u53d6\u81ea\u674e\u5b8f\u6bc5\u8001\u5e08\u673a\u5668\u5b66\u4e60\u8bfe\u7a0b\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p><center><br \/>\n  \uff08\u56fe\u7247\u622a\u53d6\u81ea\u674e\u5b8f\u6bc5\u8001\u5e08\u673a\u5668\u5b66\u4e60\u8bfe\u7a0b\uff09<br \/>\n<\/center> \u2003\u2003Conditional GAN\u4e2dgenerator\u7684\u8f93\u5165\u662f\u6210\u5bf9\u7684\u6570\u636e\uff0c\uff08\u6761\u4ef6\u6807\u7b7e\uff0c\u566a\u58f0z\uff09\uff0cgenerator\u7684\u4f5c\u7528\u662f\u751f\u6210\u5bf9\u5e94\u6761\u4ef6\u6807\u7b7e\u7684\u56fe\u7247\uff0c\u800cDiscriminator\u7684\u4f5c\u7528\u5219\u7531\u539f\u6765\u7684\u4e00\u4e2a\uff08\u5224\u65ad\u751f\u6210\u7684\u6570\u636e\u662f\u5426\u4e3a\u771f\uff09\u53d8\u4e3a\u4e24\u4e2a\uff08\u5224\u65ad\u751f\u6210\u7684\u6570\u636e\u662f\u5426\u4e3a\u771f+\u751f\u6210\u6570\u636e\u662f\u5426\u4e0e\u5bf9\u5e94\u7684\u6761\u4ef6\u6807\u7b7e\u76f8\u5339\u914d\uff09\u3002 <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/6d9cd6171b6d4a5394239db8247b3b4f.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u2003\u2003\u6240\u4ee5Dixcriminator\u5224\u65ad\u4e3a\u771f\u7684\u53ef\u80fd\u662f\uff1a\u771f\u5b9e\u7684\u56fe\u7247+\u5bf9\u5e94\u7684\u6807\u7b7e\uff1b\u800c\u5224\u65ad\u4e3a\u5047\u7684\u53ef\u80fd\u662f\uff1a\u771f\u5b9e\u7684\u56fe\u7247+\u9519\u8bef\u7684\u6761\u4ef6\u6807\u7b7e\uff0c\u751f\u6210\u7684\u56fe\u7247+\u6761\u4ef6\u6807\u7b7e\u3002<br \/> \u2003\u2003\u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u635f\u5931\u51fd\u6570\uff1a<br \/> \u2003\u2003\u5bf9\u4e8eD\u6765\u8bf4\uff1a\uff08\u5c31\u662f\u4ece\u539f\u6765\u7684\u4e24\u9879\u53d8\u4e3a\u4e86\u4e09\u9879\uff09\u5f53\u5f53\u5f53\uff01<br \/> \u2003\u2003\u2160\uff1a\u4ece\u771f\u5b9e\u6570\u636e\u96c6\u4e2d\u62bd\u6837\u51fa\u6570\u636e\u5bf9\uff08label\uff0cimage\uff09\u4e5f\u5c31\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { ( c 1 , x 1 ) , ( c 2 , x 2 ) , . . . , ( c m , x m ) } \\left\\{ \\left( c^1,x^1 \\right) ,\\left( c^2,x^2 \\right) ,...,\\left( c^m,x^m \\right) \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u2003\u2003\u2003\u2003\u5f97\u5230\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 1 m \u2211 i = 1 m log \u2061 D ( c i , x i ) \\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log D\\left( c^i,x^i \\right)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u2003\u2003\u2161\uff1a\u4ece\u771f\u5b9e\u6570\u636e\u96c6\u4e2d\u62bd\u6837\u51fa\u6570\u636e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x ^ 1 , x ^ 2 , . . . , x ^ m } \\left\\{ \\hat{x}^1,\\hat{x}^2,...,\\hat{x}^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u2003\u2003\u2003\u2003\u5f97\u5230\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 1 m \u2211 i = 1 m log \u2061 ( 1 \u2212 D ( c i , x ^ i ) ) \\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log \\left( 1-D\\left( c^i,\\hat{x}^i \\right) \\right)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u2003\u2003\u2162\uff1a\u7531\u6761\u4ef6\u6807\u7b7e\u548c\u566a\u58f0\u751f\u6210\u7684fake\u6570\u636e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x ~ 1 , x ~ 2 , . . . , x ~ m } , x ~ i = G ( c i , z i ) \\left\\{ \\tilde{x}^1,\\tilde{x}^2,...,\\tilde{x}^m \\right\\} ,\\tilde{x}^i=G\\left( c^i,z^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u2003\u2003\u2003\u2003\u5f97\u5230\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 1 m \u2211 i = 1 m log \u2061 ( 1 \u2212 D ( c i , x ~ i ) ) \\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log \\left( 1-D\\left( c^i,\\tilde{x}^i \\right) \\right)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u2003\u2003\u6240\u4ee5\uff1a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> V ~ = 1 m \u2211 i = 1 m log \u2061 D ( c i , x i ) + 1 m \u2211 i = 1 m log \u2061 ( 1 \u2212 D ( c i , x ^ i ) ) + 1 m \u2211 i = 1 m log \u2061 ( 1 \u2212 D ( c i , x ~ i ) ) \\tilde{V}=\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log D\\left( c^i,x^i \\right)}+\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log \\left( 1-D\\left( c^i,\\hat{x}^i \\right) \\right)}+\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log \\left( 1-D\\left( c^i,\\tilde{x}^i \\right) \\right)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b8 d \u2190 \u03b8 d + \u03b7 \u2207 V ~ ( \u03b8 d ) \\theta _d\\gets \\theta _d+\\eta \\nabla \\tilde{V}\\left( \\theta _d \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.17019em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03b7<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003\u90a3\u4e48\u5bf9\u4e8eG\u6765\u8bf4\u5462\uff1a<br \/> \u2160\uff1a\u566a\u58f0<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { z 1 , z 2 , . . . , z m } \\left\\{ z^1,z^2,...,z^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,\u6761\u4ef6\u6807\u7b7e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { c 1 , c 2 , . . . , c m } \\left\\{ c^1,c^2,...,c^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> V ~ = 1 m \u2211 i = 1 m log \u2061 ( D ( G ( c i , z i ) ) ) , \u03b8 g \u2190 \u03b8 g \u2212 \u03b7 \u2207 V ~ ( \u03b8 g ) \\tilde{V}=\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log \\left( D\\left( G\\left( c^i,z^i \\right) \\right) \\right)},\\theta _g\\gets \\theta _g-\\eta \\nabla \\tilde{V}\\left( \\theta _g \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.04398em;\">z<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.980548em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2063em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03b7<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u5728\u8fd9\u91cc\u7a0d\u5fae\u8865\u5145\u4e00\u4e0b\uff0c\u6211\u4eec\u521a\u521a\u8bf4\u5230\u4e86D\u7684\u4f5c\u7528\u6709\u4e24\u4e2a\u5206\u522b\u662f\u5224\u65ad\u662f\u5426\u4e3a\u771f\u4ee5\u53ca\u5224\u65ad\u6570\u636e\u4e0e\u6761\u4ef6\u6807\u7b7e\u662f\u5426\u5339\u914d\uff0c\u4f46\u662f\u8fd8\u6709\u4e00\u79cd\u89c2\u70b9\u662f\uff1a<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/aac28bca579b4603b9df71f97219aee0.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c3\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u2003\u2003\u5355\u72ec\u5224\u65ad\u6570\u636e\u662f\u5426\u4e3a\u771f\uff0c\u4ee5\u53ca\u518d\u5224\u65ad\u6570\u636e\u4e0e\u6761\u4ef6\u662f\u5426\u5339\u914d\u3002\u674e\u5b8f\u6bc5\u8001\u5e08\u89c9\u5f97\u8fd9\u6837\u66f4\u5408\u7406\uff08\u6211\u4e5f\u8fd9\u6837\u60f3\u89c9\u5f97\u54c8\u54c8\u54c8\u54c8\uff09<br \/> \u2003\u2003Conditional GAN\u5e94\u7528\u7684\u60c5\u51b5\u662f\uff1a\u7ed9\u51fa\u6587\u672c\uff0c\u751f\u6210\u5bf9\u5e94\u6587\u672c\u7684\u56fe\u7247text-to-image\uff09\u3001\u8272\u5f69\u56fe\u5230\u5b9e\u7269\u56fe\u3001\u8f6e\u5ed3\u56fe\u5230\u5b9e\u7269\u56fe\uff08image-to-image\uff09\u3001\u53bb\u9664\u566a\u58f0\u3002<\/p>\n<h3>1.2Unsupervised Conditional GAN<\/h3>\n<p>\u2003\u2003\u6211\u8fd9\u6b21\u5c1d\u8bd5\u7684\u662f\u98ce\u683c\u8f6c\u6362\uff0c\u662f\u5c06\u4e00\u79cd\u98ce\u683cA\u7684\u56fe\u7247\u8f6c\u6362\u6210\u53e6\u4e00\u79cd\u98ce\u683cB\u3002\u4e00\u79cd\u98ce\u683c\u7684\u56fe\u7247\u4f1a\u6709\u5f88\u591a\u7c7b\uff0c\u5982\u679c\u6309\u7167conditionalGAN\u7684\u601d\u60f3\u90a3\u4e48\u6570\u636e\u5bf9\u5219\u662f\u5bf9\u5e94\u7c7b\u522b\u7684\u98ce\u683cB\u7684\u56fe\u7247\uff0c\u4f46\u662f\u663e\u7136\u5982\u679c\u6211\u8981\u5c06\u771f\u5b9e\u7684\u56fe\u7247\u8f6c\u6362\u4e3a\u68b5\u9ad8\u5927\u5e08\u7684\u98ce\u683c\uff08\u5728\u8fd9\u91cc\u819c\u62dc\u4e00\u4e0b\u5927\u5e08\uff09\uff0c\u4e0d\u4e00\u5b9a\u80fd\u5728\u68b5\u9ad8\u5927\u5e08\u7684\u753b\u4f5c\u91cc\u627e\u5230\u6211\u4eec\u5bf9\u5e94\u7684\u56fe\u7247\uff0c\u800c\u4e14\u4f60\u4e5f\u4e0d\u53ef\u80fd\u8bf7\u68b5\u9ad8\u5927\u5e08\u4e3a\u4f60\u4f5c\u753b\u4e00\u5e45\u662f\u4e0d\u662f\uff0c\u9664\u975e\u4f60\u81ea\u5df1\u4f1a\u753b[\u72d7\u5934]\uff08\u5929\u554a\u67d0\u5927\u5b66\u751f\u4e3a\u5b66\u4e60\u6df1\u5ea6\u5b66\u4e60\u4eb2\u81ea\u4f5c\u753b\u7b80\u76f4\u4ee4\u95fb\u8005\u611f\u52a8\u542c\u8005\u843d\u6cea\u554a\uff09<br \/> \u2003\u2003Ok\u8bf4\u5230\u8fd9\u91cc\u5462\uff0c\u5176\u5b9e\u5c31\u662fconditionalGAN\u5df2\u7ecf\u4e0d\u9002\u7528\u8fd9\u79cd\u60c5\u51b5\u5566\uff0c\u90a3\u53ef\u5982\u4f55\u662f\u597d\u5462\uff1f\u5176\u5b9e\u521a\u624d\u7ea0\u7ed3\u7684\u70b9\u5c31\u662f\u7c7b\u522b\u7684\u95ee\u9898\uff0c\u6211\u4eec\u627e\u4e0d\u5230\u5bf9\u5e94\u7c7b\u522b\u7684\u76ee\u6807\u98ce\u683c\u7684\u7167\u7247\uff0c\u6240\u4ee5\u6211\u4eec\u80fd\u4e0d\u80fd\u4e0d\u8981\u6807\u7b7e\u5462\uff0c\u8ba9\u673a\u5668\u81ea\u5df1\u5b66\u4f1a\u76ee\u6807\u98ce\u683c\u7684\u6570\u636e\u5206\u5e03\u3002\u554a\u8fd9\uff0c\u8fd9\u4e0d\u5c31\u662f\u65e0\u76d1\u7763\u5b66\u4e60\u505a\u64c5\u957f\u5e72\u7684\u4e8b\u60c5\u561b\uff01\u5bf9\uff0c\u6240\u4ee5\u5c31\u6709\u806a\u660e\u7684\u524d\u8f88\u4eec\uff0c\u5229\u7528\u9ad8\u7ea7\u751f\u7269\u7684\u667a\u6167\u8ba9\u673a\u5668\u8fdb\u884cunsupervised conditional generation\uff0c\u671f\u95f4\u5462\u5c31\u521b\u9020\u51fa\u5927\u5927\u5c0f\u5c0f\uff0c\u591a\u591a\u5c11\u5c11\u597d\u591a\u79cdGAN\uff0c\u4e3b\u8981\u662f\u4e24\u79cd\u601d\u8def\u3002<\/p>\n<h4>No.1 Direct Transformation\uff0c\u76f4\u63a5\u8f6c\u6362<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/304fd928b0d74351b7b1e18a71eccd37.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u2003\u2003\u7b2c\u4e00\u79cd\u601d\u8def\u6700\u6709\u540d\u7684\u5c31\u662f\u6211\u4eec\u4eca\u5929\u8981\u9686\u91cd\u4ecb\u7ecd\u7684cycleGAN\u5566\uff01\uff01\u6574\u4e2a\u7f51\u7edc\u7684\u8bbe\u8ba1\u5462\u662f\u8fd9\u6837\u6ef4\uff1a<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/a26a5a8407a942dc8a7831748a1ed45b.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c5\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c5\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u2003\u2003\u6574\u4e2a\u7f51\u7edc\u8bbe\u8ba1\u4e862\u4e2aGenerators\uff0c2\u4e2aDiscriminators\u3002\u6211\u4eec\u5df2\u6709\u7684\u56fe\u7247\u6570\u636e\u5206\u5e03\u4e3aDomainX\uff0c\u60f3\u8981\u8f6c\u6362\u7684\u76ee\u6807\u98ce\u683c\u7684\u6570\u636e\u5206\u5e03\u4e3aDomainY\u3002<br \/> \u2003\u2003\u5bf9\u4e8e\u5df2\u6709\u6570\u636e\u6765\u8bf4\uff0c2\u4e2aGenerators\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G X \u2192 Y G_{X\\rightarrow Y} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5c06\u76ee\u6807\u98ce\u683c\u56fe\u50cf\u8f6c\u6362\u4e3a\u5df2\u6709\u6570\u636e\u5206\u5e03\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G X \u2192 Y G_{X\\rightarrow Y} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5c06\u751f\u6210\u7684fake\u56fe\u50cf\u518d\u8f6c\u6362\u4e3a\u539f\u6765\u7684\u56fe\u50cf\uff0c\u6211\u4eec\u60f3\u8981\u7684\u662f\u548c\u539f\u6765\u76ee\u6807\u98ce\u683c\u7684\u56fe\u50cf\u8d8a\u63a5\u8fd1\u8d8a\u597d\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> D X D_X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5224\u65ad\u751f\u6210\u7684fake\u56fe\u50cf\u662f\u5426\u5c5e\u4e8eX\u5206\u5e03\u3002<br \/> \u2003\u2003\u6211\u4eec\u5148\u6765\u8bf4\u660e\u4e00\u4e0b\u5404\u4e2a\u6570\u636e\u7b26\u53f7\u8868\u793a\u53ca\u610f\u4e49\uff1a<br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>\uff1a\u5df2\u6709\u7684\u6570\u636e\u5206\u5e03\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x i x^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a\u5df2\u6709\u7684\u6570\u636e\u6837\u672c<br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>\uff1a\u76ee\u6807\u98ce\u683c\u6570\u636e\u5206\u5e03\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y i y^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0191em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a\u5df2\u6709\u7684\u76ee\u6807\u98ce\u683c\u7684\u6570\u636e\u6837\u672c<br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G X \u2192 Y G_{X\\rightarrow Y} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a\u5c06<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e\u751f\u6210<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ~ i \\tilde{y}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0191em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G X \u2192 Y G_{X\\rightarrow Y} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u751f\u6210\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ~ i \\tilde{x}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ~ i \\tilde{y}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0191em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53c8\u7ecf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G Y \u2192 X G_{Y\\rightarrow X} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u751f\u6210\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e<br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G Y \u2192 X G_{Y\\rightarrow X} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a\u5c06<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e\u751f\u6210<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ~ i \\tilde{x}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G Y \u2192 X G_{Y\\rightarrow X} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u751f\u6210\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ~ i \\tilde{y}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0191em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ~ i \\tilde{x}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53c8\u7ecf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G X \u2192 Y G_{X\\rightarrow Y} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u751f\u6210\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e<br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> D Y D_Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a\u5224\u65ad\u662f\u5426\u5c5e\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e<br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> D X D_X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a\u5224\u65ad\u662f\u5426\u5c5e\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>\u5206\u5e03\u7684\u6570\u636e<br \/> \u2003\u2003\u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u635f\u5931\u51fd\u6570\uff1a<br \/> \u2003\u2003\u5bf9\u4e8eD\u6765\u8bf4\uff1a<br \/> \u2003\u2003\u2160\uff1a\u4ece\u5df2\u6709\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x 1 , x 2 , . . . , x m } \\left\\{ x^1,x^2,...,x^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ece\u76ee\u6807\u98ce\u683c\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y 1 , y 2 , . . . , y m } \\left\\{ y^1,y^2,...,y^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5bf9\u5e94\u751f\u6210\u7684\u751f\u6210\u7684fake\u6570\u636e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y ~ 1 , y ~ 2 , . . . , y ~ m } , y ~ i = G X \u2192 Y ( x i ) \\left\\{ \\tilde{y}^1,\\tilde{y}^2,...,\\tilde{y}^m \\right\\} ,\\tilde{y}^i=G_{X\\rightarrow Y}\\left( x^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x ~ 1 , x ~ 2 , . . . , x ~ m } , x ~ i = G Y \u2192 X ( y i ) \\left\\{ \\tilde{x}^1,\\tilde{x}^2,...,\\tilde{x}^m \\right\\} ,\\tilde{x}^i=G_{Y\\rightarrow X}\\left( y^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5f97\u5230\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> L G A N _ D ( G , D , X , Y ) = L G A N ( G X \u2192 Y , D Y , X , Y ) + L G A N ( G Y \u2192 X , D X , X , Y ) = [ 1 m \u2211 i = 1 m log \u2061 D Y ( y i ) + 1 m \u2211 i = 1 m log \u2061 ( 1 \u2212 D Y ( G X \u2192 Y ( x i ) ) ) ] + [ 1 m \u2211 i = 1 m log \u2061 D X ( x i ) + 1 m \u2211 i = 1 m log \u2061 ( 1 \u2212 D X ( G Y \u2192 X ( y i ) ) ) ] L_{GAN\\_D}\\left( G,D,X,Y \\right) =L_{GAN}\\left( G_{X\\rightarrow Y},D_Y,X,Y \\right) +L_{GAN}\\left( G_{Y\\rightarrow X},D_X,X,Y \\right) \\\\ =\\left[ \\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log D_Y\\left( y^i \\right)}+\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log \\left( 1-D_Y\\left( G_{X\\rightarrow Y}\\left( x^i \\right) \\right) \\right)} \\right] \\\\ +\\left[ \\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log D_X\\left( x^i \\right)}+\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log \\left( 1-D_X\\left( G_{Y\\rightarrow X}\\left( y^i \\right) \\right) \\right)} \\right] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.117em; vertical-align: -0.367em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><span class=\"mord mtight\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.02778em;\">D<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.367em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.40003em; vertical-align: -0.95003em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.40003em; vertical-align: -0.95003em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2003\u2003\u6240\u4ee5\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> V ~ = L G A N _ G ( G , D , X , Y ) \uff0c \u03b8 d \u2190 \u03b8 d + \u03b7 \u2207 V ~ ( \u03b8 d ) \\tilde{V}=L_{GAN\\_G}\\left( G,D,X,Y \\right)\uff0c\\theta _d\\gets \\theta _d+\\eta \\nabla \\tilde{V}\\left( \\theta _d \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.117em; vertical-align: -0.367em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><span class=\"mord mtight\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault mtight\">G<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.367em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord cjk_fallback\">\uff0c<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.17019em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03b7<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u2003\u2003\u5bf9\u4e8eG\u6765\u8bf4\uff1a<br \/> \u2003\u2003\u2160\uff1a\u4ece\u5df2\u6709\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x 1 , x 2 , . . . , x m } \\left\\{ x^1,x^2,...,x^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ece\u76ee\u6807\u98ce\u683c\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y 1 , y 2 , . . . , y m } \\left\\{ y^1,y^2,...,y^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ee5\u53ca\u5bf9\u5e94\u751f\u6210\u7684\u5404\u81ea\u7684fake\u6570\u636e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y ~ 1 , y ~ 2 , . . . , y ~ m } , y ~ i = G X \u2192 Y ( x i ) \\left\\{ \\tilde{y}^1,\\tilde{y}^2,...,\\tilde{y}^m \\right\\} ,\\tilde{y}^i=G_{X\\rightarrow Y}\\left( x^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x ~ 1 , x ~ 2 , . . . , x ~ m } , x ~ i = G Y \u2192 X ( y i ) \\left\\{ \\tilde{x}^1,\\tilde{x}^2,...,\\tilde{x}^m \\right\\} ,\\tilde{x}^i=G_{Y\\rightarrow X}\\left( y^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5f97\u5230\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> L G A N _ G ( G , D , X , Y ) = L G A N ( G X \u2192 Y , D Y , X ) + L G A N ( G Y \u2192 X , D X , Y ) = 1 m \u2211 i = 1 m log \u2061 D Y ( G X \u2192 Y ( x i ) ) + 1 m \u2211 i = 1 m log \u2061 D X ( G Y \u2192 X ( y i ) ) L_{GAN\\_G}\\left( G,D,X,Y \\right) =L_{GAN}\\left( G_{X\\rightarrow Y},D_Y,X \\right) +L_{GAN}\\left( G_{Y\\rightarrow X},D_X,Y \\right) \\\\ =\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log D_Y\\left( G_{X\\rightarrow Y}\\left( x^i \\right) \\right)}+\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\log D_X\\left( G_{Y\\rightarrow X}\\left( y^i \\right) \\right)} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.117em; vertical-align: -0.367em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><span class=\"mord mtight\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault mtight\">G<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.367em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mop\">lo<span style=\"margin-right: 0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2003\u2003\u2161\uff1a\u4ece\u5df2\u6709\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x 1 , x 2 , . . . , x m } \\left\\{ x^1,x^2,...,x^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ece\u76ee\u6807\u98ce\u683c\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y 1 , y 2 , . . . , y m } \\left\\{ y^1,y^2,...,y^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ee5\u53ca\u6700\u540ereconstruct\u7684fake\u6570\u636e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x ~ 1 , x ~ 2 , . . . , x ~ m } , x ~ i = G Y \u2192 X ( G X \u2192 Y ( x i ) ) \\left\\{ \\tilde{x}^1,\\tilde{x}^2,...,\\tilde{x}^m \\right\\} ,\\tilde{x}^i=G_{Y\\rightarrow X}\\left( G_{X\\rightarrow Y}\\left( x^i \\right) \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y ~ 1 , y ~ 2 , . . . , y ~ m } , y ~ i = G X \u2192 Y ( G Y \u2192 X ( y i ) ) \\left\\{ \\tilde{y}^1,\\tilde{y}^2,...,\\tilde{y}^m \\right\\} ,\\tilde{y}^i=G_{X\\rightarrow Y}\\left( G_{Y\\rightarrow X}\\left( y^i \\right) \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5f97\u5230\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> L c y c l e ( G X \u2192 Y , G Y \u2192 X , X , Y ) = L c y c l e ( G X \u2192 Y , G Y \u2192 X , X ) + L c y c l e ( G X \u2192 Y , G Y \u2192 X , Y ) = 1 m \u2211 i = 1 m \u2225 G Y \u2192 X ( G X \u2192 Y ( x i ) ) \u2212 x i \u2225 L 1 + 1 m \u2211 i = 1 m \u2225 G X \u2192 Y ( G Y \u2192 X ( y i ) ) \u2212 y i \u2225 L 1 L_{cycle}\\left( G_{X\\rightarrow Y},G_{Y\\rightarrow X},X,Y \\right) =L_{cycle}\\left( G_{X\\rightarrow Y},G_{Y\\rightarrow X},X \\right) +L_{cycle}\\left( G_{X\\rightarrow Y},G_{Y\\rightarrow X},Y \\right) \\\\ =\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\left\\| G_{Y\\rightarrow X}\\left( G_{X\\rightarrow Y}\\left( x^i \\right) \\right) -x^i \\right\\| _{L1}+}\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\left\\| G_{X\\rightarrow Y}\\left( G_{Y\\rightarrow X}\\left( y^i \\right) \\right) -y^i \\right\\| _{L1}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mord mathdefault mtight\">e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mord mathdefault mtight\">e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mord mathdefault mtight\">e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.078621em;\"><span class=\"\" style=\"top: -2.30029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">L<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.39971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">+<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.078621em;\"><span class=\"\" style=\"top: -2.30029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">L<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.39971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2003\u2003\u4ece\u5df2\u6709\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x 1 , x 2 , . . . , x m } \\left\\{ x^1,x^2,...,x^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ece\u76ee\u6807\u98ce\u683c\u6570\u636e\u96c6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>domain\u62bd\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y 1 , y 2 , . . . , y m } \\left\\{ y^1,y^2,...,y^m \\right\\} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ee5\u53ca\u5bf9\u5e94\u751f\u6210\u7684\u5404\u81ea\u7684fake\u6570\u636e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { y ~ 1 , y ~ 2 , . . . , y ~ m } , y ~ i = G X \u2192 Y ( x i ) \\left\\{ \\tilde{y}^1,\\tilde{y}^2,...,\\tilde{y}^m \\right\\} ,\\tilde{y}^i=G_{X\\rightarrow Y}\\left( x^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> { x ~ 1 , x ~ 2 , . . . , x ~ m } , x ~ i = G Y \u2192 X ( y i ) \\left\\{ \\tilde{x}^1,\\tilde{x}^2,...,\\tilde{x}^m \\right\\} ,\\tilde{x}^i=G_{Y\\rightarrow X}\\left( y^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">{<br \/>\n        <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">}<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5f97\u5230\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> L i d e n t i t y ( G X \u2192 Y , G Y \u2192 X , X , Y ) = L i d e n t i t y ( G X \u2192 Y , X ) + L i d e n t i t y ( G Y \u2192 X , Y ) = 1 m \u2211 i = 1 m \u2225 G X \u2192 Y ( x i ) \u2212 x i \u2225 L 1 + 1 m \u2211 i = 1 m \u2225 G Y \u2192 X ( y i ) \u2212 y i \u2225 L 1 L_{identity}\\left( G_{X\\rightarrow Y},G_{Y\\rightarrow X},X,Y \\right) =L_{identity}\\left( G_{X\\rightarrow Y},X \\right) +L_{identity}\\left( G_{Y\\rightarrow X},Y \\right) \\\\ =\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\left\\| G_{X\\rightarrow Y}\\left( x^i \\right) -x^i \\right\\|}_{L1}+\\frac{1}{m}\\sum\\nolimits_{i=1}^m{\\left\\| G_{Y\\rightarrow X}\\left( y^i \\right) -y^i \\right\\|}_{L1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">d<\/span><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">d<\/span><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">d<\/span><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.078621em;\"><span class=\"\" style=\"top: -2.30029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">L<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.39971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">m<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol large-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10429em;\"><span class=\"\" style=\"top: -2.10029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.5029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.874664em;\"><span class=\"\" style=\"top: -3.113em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.86199em;\"><span class=\"\" style=\"top: -2.25599em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -2.86199em;\"><span class=\"pstrut\" style=\"height: 2.606em;\"><\/span><span class=\"delimsizinginner delim-size1\"><span class=\"\">\u2225<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35001em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.078621em;\"><span class=\"\" style=\"top: -2.30029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">L<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.39971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2003\u2003\u6240\u4ee5\uff1a<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> V ~ = L G A N _ G ( G , D , X , Y ) + L c y c l e ( G X \u2192 Y , G Y \u2192 X , X , Y ) + L i d e n t i t y ( G X \u2192 Y , G Y \u2192 X , X , Y ) \\tilde{V}=L_{GAN\\_G}\\left( G,D,X,Y \\right) +L_{cycle}\\left( G_{X\\rightarrow Y},G_{Y\\rightarrow X},X,Y \\right) +L_{identity}\\left( G_{X\\rightarrow Y},G_{Y\\rightarrow X},X,Y \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.92019em; vertical-align: 0em;\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.117em; vertical-align: -0.367em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">G<\/span><span class=\"mord mathdefault mtight\">A<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.10903em;\">N<\/span><span class=\"mord mtight\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault mtight\">G<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.367em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord mathdefault\">G<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"mord mathdefault mtight\">c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mord mathdefault mtight\">e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">d<\/span><span class=\"mord mathdefault mtight\">e<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mord mathdefault mtight\">t<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03b8 g \u2190 \u03b8 g \u2212 \u03b7 \u2207 V ~ ( \u03b8 g ) \\theta _g\\gets \\theta _g-\\eta \\nabla \\tilde{V}\\left( \\theta _g \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.980548em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.980548em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2063em; vertical-align: -0.286108em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">\u03b7<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.92019em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -3.60233em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.25em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">g<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003\u5f53\u7136\u5566\uff0c\u4efb\u4f55\u7f51\u7edc\u90fd\u4e0d\u662f\u7edd\u5bf9\u5b8c\u7f8e\u7684\uff0c\u540c\u6837\u7684cycleGAN\u4e5f\u5b58\u5728\u7740\u95ee\u9898stenography\uff0c\u6709\u4eba\u53d1\u73b0\u5462cycleGAN\u4f1a\u628ainput\u7684\u5185\u5bb9\u85cf\u8d77\u6765\uff0coutput\u65f6\u518d\u628a\u5185\u5bb9\u5448\u73b0\u51fa\u6765\u3002\u4ee5<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x i \u2192 y ^ i \u2192 x ^ i x^i\\rightarrow \\hat{y}^i\\rightarrow \\hat{x}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0191em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">^<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u4f8b\uff0c\u5728\u751f\u6210\u4e2d\u95f4\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ^ i \\hat{y}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0191em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">^<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u65f6\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G X \u2192 Y G_{X\\rightarrow Y} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6709\u5f88\u5f3a\u7684\u80fd\u529b\u628a\u4fe1\u606f\u85cf\u5728\u4eba\u770b\u4e0d\u5230\u7684\u5730\u65b9\uff0c\u5728\u6062\u590d\u7684\u65f6\u5019<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> G Y \u2192 X G_{Y\\rightarrow X} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u518d\u628a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ^ i \\hat{x}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5448\u73b0\u51fa\u6765\u3002\u8fd9\u6837\u7684\u8bddcycle consistency\u53ef\u80fd\u5c31\u6ca1\u6709\u610f\u4e49\uff0c\u56e0\u4e3a\u5c3d\u7ba1<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x i x^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x i x^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.824664em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u76f8\u4f3c\uff0c\u4f46\u4e2d\u95f4\u771f\u6b63\u4f20\u5165<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> D Y D_Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">D<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.02778em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ^ i \\hat{y}^i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0191em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">^<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53ef\u80fd\u5df2\u7ecf\u5f88\u4e0d\u540c\u4e86\u3002<\/p>\n<h4>No.2 Projection to Common Spcae\uff0c\u5148\u7f16\u7801\u51fa\u62bd\u8c61\u7279\u5f81\uff0c\u5728\u89e3\u7801\u8f6c\u6362\u4e3a\u56fe\u50cf<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/1c590b9f3da44270b5eeed0670e9c5d0.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c6\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c6\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u2003\u2003\u7b2c\u4e8c\u79cd\u4e5f\u6709\u5f88\u591a\u7684\u65b9\u6cd5\uff0c\u5728\u8fd9\u91cc\u5c31\u4e0d\u4ecb\u7ecd\u5566\u3002<\/p>\n<h2>\u4e8c\u3001\u4ee3\u7801\u90e8\u5206<\/h2>\n<p>\u2003\u2003\u539f\u7406\u90e8\u5206\u5df2\u5206\u6790\u5b8c\uff0c\u6211\u4eec\u6765\u770b\u770b\u7a0b\u5e8f\u90e8\u5206\u662f\u600e\u4e48\u5b9e\u73b0\u7684\u5462<br \/> \u2003\u2003\u6211\u73b0\u5728\u5df2\u7ecf\u770b\u8fc7\u5e76\u5904\u7406\u8fc7\u51e0\u4e2a\u5b8c\u6574\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u795e\u7ecf\u7f51\u7edc\u5566\uff0c\u6bcf\u6b21\u770b\u7684\u65f6\u5019\u90fd\u4f1a\u5b66\u5230\u5f88\u591a\u5f88\u591a\uff0c\u9664\u4e86\u57fa\u672c\u7684\u6846\u67b6\u5462\uff0c\u6709\u65f6\u5019\u80fd\u611f\u89c9\u5230\u4f5c\u8005\u7684\u5de7\u601d\uff0c\u4e00\u4e9b\u7ec6\u8282\u6709\u82b1\u5fc3\u601d\u5728\u4e0a\u9762\uff0c\u5f88\u8ba9\u4eba\u60ca\u53f9\uff01\uff01\u800c\u4e14\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u9762\u5bf9\u81ea\u5df1\u4e0d\u61c2\u7684\u51fd\u6570\u8fd8\u6709\u7f16\u7a0b\u7684\u601d\u8def\u5462\uff0c\u4e00\u70b9\u70b9\u5206\u6790\u5c31\u4f1a\u6709\u62bd\u4e1d\u5265\u8327\uff0c\u6309\u56fe\u7d22\u9aa5\uff0c\u6700\u540e\u604d\u7136\u5927\u609f\u7684\u611f\u89c9\uff01\u90fd\u8bf4\u5174\u8da3\u662f\u6700\u597d\u7684\u8001\u5e08\uff0c\u6211\u73b0\u5728\u6df1\u4ee5\u4e3a\u7136\uff0c\u4e4b\u524d\u6211\u603b\u89c9\u5f97\u51e1\u4e8b\u90fd\u8981\u7cfb\u7edf\u7684\u5b66\u4e60\uff0c\u4f46\u4e8b\u5b9e\u4e0a\u73b0\u5728\u7684\u77e5\u8bc6\u66f4\u591a\u7684\u662f\u8981\u9760\u81ea\u5df1\u5462\u7531\u70b9\u53ca\u9762\u9010\u6b65\u63a2\u7d22\uff0c\u800c\u4e14\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u53d1\u73b0\u4e86\u6570\u5b66\u601d\u60f3\u5e26\u6765\u7684\u7f8e\u5999\uff0c\u771f\u7684\u89c9\u5f97\u5f88\u795e\u5947\uff01\u597d\u5566\u8bf4\u56de\u7a0b\u5e8f\u90e8\u5206\u5427\u3002<\/p>\n<h3>2.1\u8d85\u53c2\u6570<\/h3>\n<p>\u2003\u2003\u6211\u6b64\u6b21\u53c2\u8003\u7684\u7a0b\u5e8f\u662f\u8bba\u6587\u63d0\u4f9b\u7684\u4ee3\u7801\uff08\u5fcd\u4e0d\u4f4f\u60ca\u53f9\uff1a\u771f\u7684\u662f\u5199\u5f97\u5f88\u597d\u5462\uff01\uff09\u548c\u4e0a\u6b21\u5b9e\u73b0\u7684DCGAN\u751f\u6210\u4e8c\u6b21\u5143\u5934\u50cf\u7684\u601d\u8def\u662f\u4e00\u6837\u7684\uff0c\u4e5f\u662f\u5c06\u8d85\u53c2\u6570\u5199\u8fdb\u7c7b\u4e2d\uff0c\u4f46\u662f\u8bba\u6587\u4ee3\u7801\u4e0d\u662f\u81ea\u5b9a\u4e49\u7c7b\uff0c\u800c\u662f\u8c03\u7528argparse\u5e93\u8fdb\u884c\u521d\u59cb\u5316\u3002<\/p>\n<h3>2.2\u6570\u636e\u9884\u5904\u7406<\/h3>\n<p>\u2003\u2003\u662f\u5728__getitem__()\u51fd\u6570\u91cc\u8fdb\u884c\u4e86\u6539\u5199\uff0c\u533a\u5206\u51fa\u4e86<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X X <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span>domain\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> Y Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>domain\u7684\u6570\u636e\uff0c\u8fd4\u56de\u5b57\u5178<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> X , Y X,Y <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span>\u4f5c\u4e3a\u952e\u540d\u3002<\/p>\n<h3>2.3\u7f51\u7edc<\/h3>\n<p>\u2003\u2003\u7f51\u7edc\u8fd9\u90e8\u5206\u4e5f\u662f\u6211\u89c9\u5f97\u5f88\u65b0\u5947\u7684\u5199\u6cd5\u3002\u53c2\u8003\u4ee3\u7801\u6ca1\u6709\u6309\u7167\u5e38\u89c4\u7684\u4e00\u5c42\u4e00\u5c42\u5217\u5728Sequential()\u4e2d\uff0c\u800c\u662f\u628a\u4e00\u5757\u4e00\u5757\u653e\u5728blocklist\u4e2d\u8d4b\u4e88\u4e00\u4e2a\u53d8\u91cfmodel\uff0c\u6709\u7684\u5757\u8981\u597d\u51e0\u6b21\uff0c\u5c31\u653e\u5728for\u5faa\u73af\u91cc\uff0cmodel+=blocklist\u5ef6\u957fmodellist\uff0c\u6700\u540e\u6267\u884cSequential(*model)<br \/> \u53e6\u5199\u4e86\u51fd\u6570def Create_nets()\uff0c\u662f\u4e0d\u662f\u770b\u540d\u5b57\u5c31\u77e5\u9053\u5566\uff01\u5bf9\u5427\uff0c\u5c31\u662f\u5728\u8fd9\u91cc\u628aGenerator\u548cDiscriminator\u5b9e\u4f8b\u5316\u3002<br \/> \u2003\u2003\u53ef\u80fd\u662f\u6211\u5b64\u964b\u5be1\u95fb\u4e86\uff0c\u4f46\u662f\u770b\u5230\u8fd9\u91cc\u771f\u7684\u633a\u5174\u594b\u7684\uff0c\u5c31\u89c9\u5f97\u54a6\u8fd8\u80fd\u8fd9\u6837\u5199\uff01\u771f\u7684\u662f\u7b80\u6d01\u6613\u61c2\u3002<\/p>\n<h3>2.4\u4f18\u5316\u5668\u548c\u635f\u5931\u51fd\u6570<\/h3>\n<p>\u2003\u2003\u8fd8\u6709\u8fd9\u91cc\uff01\u548cdef Create_nets()\u7684\u60f3\u6cd5\u4e00\u6837\uff0c\u4f18\u5316\u5668\u548c\u635f\u5931\u51fd\u6570\u5355\u72ec\u5199\u4e86\u51fd\u6570\u8fdb\u884c\u5b9e\u4f8b\u5316\u3002\u53c2\u8003\u4ee3\u7801\u8fd8\u5199\u4e86\u66f4\u65b0\u5b66\u4e60\u7387\u7684\u51fd\u6570\uff0c\u4e4b\u524d\u770b\u7684\u4ee3\u7801\u6ca1\u6709\u8fd9\u4e00\u6b65\u5462\u3002<br \/> \u2003\u2003\u53c2\u8003\u4ee3\u7801\u6709\u4e00\u4e2autils\u7684py\u6587\u4ef6\uff0c\u7ed9\u4eba\u611f\u89c9\u50cf\u662f\u5c0f\u5de5\u5177\u5305\u54c8\u54c8\u54c8\uff0c\u4e00\u4e9b\u7ed8\u56fe\u7b49\u51fd\u6570\u5c31\u653e\u5728\u8fd9\u91cc\u3002\u8fd9\u4e2a\u4f5c\u8005\u5f88\u7cbe\u81f4\u5462\uff0c\u5c0f\u4e1c\u897f\u4e5f\u4e0d\u4e71\u653e\u6536\u62fe\u5f97\u6574\u6574\u9f50\u9f50\u54c8\uff0c\u6211\u540e\u6765\u5199\u7684\u7ed8\u5236Loss\u56fe\u50cf\u7684\u7684\u51fd\u6570\u4e5f\u653e\u5728\u8fd9\u91cc\u5566\uff01<\/p>\n<h2>\u4e09\u3001\u8fd0\u884c\u7ed3\u679c<\/h2>\n<h3>3.1CUDA\u5360\u6ee1\u95ee\u9898<\/h3>\n<p>\u2003\u2003OK\u8fd9\u4e0b\u6211\u4eec\u4ee3\u7801\u90e8\u5206\u4e5f\u5206\u6790\u5b8c\u5566\uff0c\u90a3\u4e48\u7a0b\u5e8f\u8fd0\u884c\u540e\u7684\u7ed3\u679c\u600e\u4e48\u6837\u5462\uff1f<br \/> \u2003\u2003\u9996\u5148\u662f\uff01\uff01\u5728\u6211\u7684\u7535\u8111\u4e0a\u662f\u6839\u672c\u8dd1\u4e0d\u901a\u6ef4\uff0c\u4f46\u7136\u6211\u5f88\u9707\u60ca\u7684\u662f601\u670d\u52a1\u5668\u4e0a\u4e5f\u8dd1\u4e0d\u4e86\uff01\u4f46\u662f\u6211\u4e00\u770b\u5b83\u7684batch\u53ea\u67091\u5440\uff0c\u540e\u6765\u60f3Discriminator\u548cGenerator\u7ffb\u4e86\u4e24\u500d\uff0c\u800c\u4e14\u751f\u6210\u7684\u56fe\u7247\u662f256*256[\u9707\u60ca\u8138]\uff0c\u90a3\u53c2\u6570\u91cf\u53ef\u5c31\u592a\u591a\u4e86\uff0c\u800c\u4e14Discriminator\u548cGenerator\u90fd\u6709\u597d\u591a\u5c42\uff0c\u4e4b\u524d\u7684DCGAN\u662f\u6ca1\u6cd5\u6bd4\u7684\u3002\u4e8e\u662f\u679c\u65ad\u4fee\u6539\u751f\u6210\u56fe\u7247\u7684size\u3002<br \/> \u2003\u2003\u4e0b\u9762\u662f\u6211\u8bb0\u5f55\u7684\u4e0d\u540csize\u4e0b\u5360\u7528GPU\uff0c\u4ee5\u53ca\u8bad\u7ec3\u901f\u5ea6<br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/ffd3567c0075441691b8457b0fc5f7a7.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c7\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c7\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> \u540e\u6765\u6211\u9009\u7528\u7684\u662fbatch:45<\/p>\n<h3>3.2\u8bad\u7ec3\u8fc7\u7a0b<\/h3>\n<p>\u2003\u2003\u5728\u8fd9\u91cc\u8bf4\u660e\u4e00\u4e0bLoss\u56fe\u4e2d\u7684\u7b2c\u4e8c\u4e2a\u5b50\u56fe\u753b\u7684\u662fLoss_GAN\uff0cLoss_cycle\uff0cLoss_identity\uff0c\u5b50\u56fe\u4e0a\u7684title\u5fd8\u8bb0\u4fee\u6539\u4e86\u545c\u545c\u3002<br \/> \u2003\u2003\u751f\u6210\u7684\u56fe\u72478x4\uff0c\u4e00\u884c4\u4e2a\u662f\u62bd\u53d64\u4e2a\u6837\u4f8b\uff0c\u4e00\u5217\u4ece\u4e0a\u5f80\u4e0b\u662f\uff1a<br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y i ( y i _ Y ) y^i\\left( y^i\\_Y \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ~ i ( y i _ X ) = G Y \u2192 X ( y i ) \\tilde{x}^i\\left( y^i\\_X \\right) =G_{Y\\rightarrow X}\\left( y^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ~ i ( y i _ R Y ) = G X \u2192 Y ( G Y \u2192 X ( y i ) ) \\tilde{y}^i\\left( y^i\\_RY \\right) =G_{X\\rightarrow Y}\\left( G_{Y\\rightarrow X}\\left( y^i \\right) \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ^ i ( x i _ X ) = G Y \u2192 X ( x i ) \\hat{x}^i\\left( x^i\\_X \\right) =G_{Y\\rightarrow X}\\left( x^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">^<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x i ( x i _ X ) x^i\\left( x^i\\_X \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ~ i ( x i _ Y ) = G X \u2192 Y ( x i ) \\tilde{y}^i\\left( x^i\\_Y \\right) =G_{X\\rightarrow Y}\\left( x^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">~<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> x ~ i ( x i _ R X ) = G Y \u2192 X ( G X \u2192 Y ( x i ) ) \\tilde{x}^i\\left( x^i\\_RX \\right) =G_{Y\\rightarrow X}\\left( G_{X\\rightarrow Y}\\left( x^i \\right) \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -3.35em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.22222em;\">~<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u2003\u2003<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> y ^ i ( y i _ Y ) = G X \u2192 Y ( y i ) \\hat{y}^i\\left( y^i\\_Y \\right) =G_{X\\rightarrow Y}\\left( y^i \\right) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><\/span><\/span><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em;\">^<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.19444em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin-right: 0.02778em;\">_<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.22222em;\">Y<\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.20001em; vertical-align: -0.35001em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">G<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.328331em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.07847em;\">X<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.22222em;\">Y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.824664em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>\uff081\uff09Epoch:10<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/3f0a4e4bee7b47cab845ac5786cafbc3.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/d56589f3740a49fe92929ce18606b9d7.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4>\uff082\uff09Epoch:20<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/636b3aa3f4f84ea7b65670fc333e88f9.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/d0974d832c434863a29f7a0f7dd83121.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c11\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c11\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4>\uff083\uff09Epoch:50<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/35147e93b52c4cdab5d94cacbe552590.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c12\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c12\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/89217939310e4b408b572ac53c53ef89.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c13\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c13\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4>\uff084\uff09Epoch:100<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/c821f20f85bc4c68978e13d2d06d6c74.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c14\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c14\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/45156fc7cc3446f29206f0b9cb412eed.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c15\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c15\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4>\uff085\uff09Epoch:200<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/34c38aa2ccca428284463b84f3b38288.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c16\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c16\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><br \/> <img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/14211832f87f4b0ebee41f07cd23a496.png#pic_center\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c17\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c17\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4>\uff086\uff09\u6c47\u603b<\/h4>\n<table>\n<thead>\n<tr>\n<th>Epoch<\/th>\n<th>LD_LG\u548cLG_Lcycle_Lidentity<\/th>\n<th>Real_Fake<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>10<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/b406a00a3bce417681dc099061d72c6b.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/a5cf2a8981974938a22357779b389d65.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c19\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c19\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<\/tr>\n<tr>\n<td>20<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/f9c9adb9bbba4ad9990efc4d53f622bd.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c20\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c20\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/7680732f85704bf98a45bcb68b21076e.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c21\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c21\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<\/tr>\n<tr>\n<td>50<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/59e699c124ba4f5599448d7c0e033bfc.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c22\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c22\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/d5278708526c455f94243acd0cea1267.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c23\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c23\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<\/tr>\n<tr>\n<td>100<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/2315897280324eb4a14f04bd2fee3d4b.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c24\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c24\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/2a6a7ae127bf41c1a489920a609ef9b0.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c25\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c25\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<\/tr>\n<tr>\n<td>200<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/08a0d34cfe3d42009feae31afb498934.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c26\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c26\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/71cf0d08e97b4e5ab1a4f5df83be4f91.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90 (https:\/\/mushiming.com\/)  \u7b2c27\u5f20\" title=\"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90  \u7b2c27\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u2003\u2003\u8fd9\u6b21\u8bd5\u9a8c\uff0c\u4e5f\u662f\u590d\u73b0\u4ee3\u7801\uff0c\u6ca1\u6709\u8fdb\u884c\u8c03\u53c2\u7684\u5de5\u4f5c\u3002\u53ef\u4ee5\u770b\u5230\u968f\u7740\u8bad\u7ec3\u6d4b\u8bd5\u7684\u589e\u591a\uff0c\u98ce\u683c\u8fc1\u79fb\u7684\u6548\u679c\u8d8a\u6765\u8d8a\u597d\u3002\u800c\u4e14Loss\u4e5f\u662f\u5728\u6309\u7167\u671f\u671b\u7684\u5728\u51cf\u5c0f\uff0c\u4f46\u8bad\u7ec3\u5230100epoch\u548c200epoch\u7684\u65f6\u5019Loss\u6709\u4e0a\u5347\u7684\u8d8b\u52bf\uff0c\u6b64\u65f6\u5e94\u8be5\u662f\u6a21\u578b\u8bad\u7ec3\u5230\u4e00\u5b9a\u7a0b\u5ea6\u4e4b\u540e\u51fa\u73b0\u7684\u4e0d\u7a33\u5b9a\uff0c\u4e0d\u518d\u968f\u7740\u68af\u5ea6\u66f4\u65b0\u800c\u8fdb\u884c\u51cf\u5c0f\u3002<\/p>\n<h2>\u56db\u3001\u5c0f\u7ed3<\/h2>\n<p>\u2003\u2003\u4ece\u6700\u5f00\u59cb\u5b9e\u4e60\u5bf9GAN\u4e00\u77e5\u534a\u89e3\uff0c\u5230\u73b0\u5728\u6bd4\u8f83\u6e05\u695aGAN\u7684\u7f51\u7edc\u7ed3\u6784\u4ee5\u53ca\u539f\u7406\uff0c\u800cGAN\u7684\u4e24\u5927\u5e94\u7528\u5206\u7c7b\u4ee5\u53ca\u751f\u6210\u6570\u636e\u4e5f\u90fd\u8fdb\u884c\u4e86\u5c1d\u8bd5\uff08\u4e0d\u77e5\u9053\u8fd9\u91cc\u8bf4\u7684\u5bf9\u4e0d\u5bf9\u563b\u563b\uff09\u6536\u83b7\u5f88\u591a\u5f88\u591a\u3002\u800c\u4e14\u6700\u6700\u5f00\u59cb\uff0c\u81ea\u5df1\u7b97\u662f\u91ce\u8def\u5b50\u5bf9\u6df1\u5ea6\u5b66\u4e60\u7684\u5c1d\u8bd5\u4e1c\u4e00\u6994\u5934\u897f\u4e00\u68d2\u69cc\uff0c\u4e0d\u6210\u4f53\u7cfb\uff0c\u73b0\u5728\u56de\u8fc7\u5934\u770b\u81ea\u5df1\u4e5f\u662f\u8d70\u4e86\u4e00\u4e9b\u5f2f\u8def\u54e6\u54c8\u54c8\u54c8\uff0c\u4e0d\u8fc7\u73b0\u5728\u5462\uff0c\u5df2\u7ecf\u6162\u6162\u77e5\u9053\u5982\u679c\u4e4b\u540e\u8fd8\u7ee7\u7eed\u5b66\u4e60\u6df1\u5ea6\u5b66\u4e60\u7684\u5185\u5bb9\u5e94\u8be5\u8981\u600e\u4e48\u505a\u5566\uff01\uff01\u8fd9\u4e00\u9636\u6bb5\u7684\u5b66\u4e60\u6211\u51c6\u5907\u6682\u544a\u4e00\u6bb5\u843d\uff0c\u4e4b\u540e\u8fd8\u4f1a\u5e26\u7740\u6d53\u539a\u7684\u5174\u8da3\u7ee7\u7eed\u5b66\u4e60\u4e0b\u53bb\uff01<\/p>\n<h2>\u4e94\u3001\u76f8\u5173\u4ee3\u7801\u53ca\u53c2\u8003\u8d44\u6599<\/h2>\n<blockquote>\n<p>\u8bba\u6587\u4ee3\u7801\uff1ahttps:\/\/codechina.csdn.net\/mirrors\/junyanz\/pytorch-cyclegan-and-pix2pix?utm_source=csdn_github_accelerator<br \/> \u8bba\u6587\u6570\u636e\u96c6\uff1ahttps:\/\/people.eecs.berkeley.edu\/~taesung_park\/CycleGAN\/datasets\/<br \/> \u8bba\u6587\uff1ahttps:\/\/arxiv.org\/pdf\/1508.06576.pdf<\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"python\u56fe\u50cf\u98ce\u683c\u8fc1\u79fb_pytorch\u6e05\u534e\u955c\u50cf\u6e90\u6587\u7ae0\u76ee\u5f55\u4e00\u3001CycleGAN\uff08CGAN\uff09\u539f\u74061.1ConditionalGAN1.2UnsupervisedConditionalGANNo....","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/4930"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=4930"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/4930\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=4930"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=4930"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=4930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}