{"id":1054,"date":"2022-06-20T17:16:47","date_gmt":"2022-06-20T09:16:47","guid":{"rendered":"http:\/\/175.24.184.226\/?p=1054"},"modified":"2022-06-20T17:19:01","modified_gmt":"2022-06-20T09:19:01","slug":"%e7%90%86%e8%a7%a3%e6%b7%b1%e5%ba%a6%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%92%8c%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"\/?p=1054","title":{"rendered":"\u7406\u89e3\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u548c\u6df1\u5ea6\u5b66\u4e60"},"content":{"rendered":"<p><a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\">\u5218\u5229\u521a<\/a><\/p>\n<p><a href=\"http:\/\/gcl.ustc.edu.cn\/\">\u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\u56fe\u5f62\u4e0e\u51e0\u4f55\u8ba1\u7b97\u5b9e\u9a8c\u5ba4<\/a><\/p>\n<p><a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\">http:\/\/staff.ustc.edu.cn\/~lgliu<\/a><\/p>\n<p>\u539f\u6587\u94fe\u63a5\uff1a <a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.html\">http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.html<\/a><\/p>\n<h2>\u3010\u7eea\u8a00\u3011<\/h2>\n<p>\u8fd1\u5e74\u6765\uff0c\u4eba\u5de5\u667a\u80fd\uff08Artificial Intelligence, AI\uff09\u548c\u6df1\u5ea6\u5b66\u4e60\uff08Deep Learning, DL\uff09\u975e\u5e38\u706b\u7206\uff0c\u5728\u5404\u4e2a\u9886\u57df\u5f97\u5230\u4e86\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u5728\u7b14\u8005\u6240\u4ece\u4e8b\u7684<a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/CG\/What_is_CG.htm\">\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66<\/a>\u9886\u57df\uff0c\u4e5f\u51fa\u73b0\u4e86\u8d8a\u6765\u8d8a\u591a\u7684\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u6765\u89e3\u51b3\u5404\u79cd\u95ee\u9898\u7684\u7814\u7a76\u5de5\u4f5c\u30022018\u5e747\u6708\u521d\uff0c\u7b14\u8005\u9996\u6b21\u5728\u7b2c\u4e03\u5c4a<a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Courses\/SummerSchool\/USTC-summer-school.html\">\u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\u300a\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u524d\u6cbf\u300b\u6691\u671f\u8bfe\u7a0b<\/a>\u4e0a\u8bb2\u6388\u548c\u5206\u4eab\u4e86\u7b14\u8005\u4ece\u6570\u5b66\uff08\u51fd\u6570\u903c\u8fd1\u8bba\uff09\u7684\u89d2\u5ea6\u6765\u5bf9\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff08Deep Neural Network, DNN\uff09\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u8fdb\u884c\u7406\u89e3\u3002\u4e4b\u540e\uff0c\u4e0d\u65ad\u6709\u5b66\u751f\u6765\u5411\u7b14\u8005\u8fdb\u4e00\u6b65\u8be2\u95ee\u548c\u4ea4\u6d41\u6709\u5173\u8d44\u6599\u548c\u95ee\u9898\u3002\u4e3a\u4e86\u4f7f\u5b66\u751f\u4eec\u80fd\u591f\u66f4\u597d\u3001\u66f4\u5feb\u7406\u89e3\u548c\u4f7f\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u548c\u6df1\u5ea6\u5b66\u4e60\uff0c\u7279\u64b0\u5199\u6b64\u6587\u3002<\/p>\n<p>\u672c\u6587\u7684\u76ee\u7684\u662f\u5e2e\u52a9\u975e\u4eba\u5de5\u667a\u80fd\u9886\u57df\u7684\u5b66\u751f\uff08\u4e3b\u8981\u662f\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u9886\u57df\u7684\u5b66\u751f\u53ca\u7b14\u8005\u7684\u5b66\u751f\uff09\u6765\u641e\u61c2\u6df1\u5ea6\u5b66\u4e60\uff08\u8fd9\u91cc\u6307\u72ed\u4e49\u7684\u6df1\u5ea6\u5b66\u4e60\uff0c\u5373\u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\uff09\u7684\u57fa\u672c\u6982\u5ff5\u548c\u65b9\u6cd5\u3002\u7b14\u8005\u5c1d\u8bd5\u7528\u901a\u4fd7\u7684\u8bed\u8a00\uff0c\u4ece\u51fd\u6570\u903c\u8fd1\u8bba\u7684\u89d2\u5ea6\u6765\u9610\u91ca\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u672c\u8d28\u3002\u7531\u4e8e\u7b14\u8005\u7684\u4e3b\u8981\u7814\u7a76\u9886\u57df\u4e3a<a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/CG\/What_is_CG.htm\">\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66<\/a>\uff0c\u800c\u975e\u4eba\u5de5\u667a\u80fd\u9886\u57df\uff0c\u56e0\u6b64\u672c\u6587\u4ec5\u4ec5\u4e3a\u7b14\u8005\u4ece\u5916\u884c\u7684\u89d2\u5ea6\u5bf9\u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u7c97\u6d45\u7406\u89e3\uff0c\u800c\u975e\u4eba\u5de5\u667a\u80fd\u9886\u57df\u5bf9DNN\u548c\u6df1\u5ea6\u5b66\u4e60\u7684\u6743\u5a01\u89e3\u91ca\u3002\u56e0\u800c\uff0c\u7b14\u8005\u5bf9\u5176\u4e2d\u7684\u6709\u4e9b\u5185\u5bb9\u7684\u7406\u89e3\u662f\u6709\u9650\u7684\uff0c\u751a\u81f3\u662f\u6709\u8bef\u7684\u3002\u5982\u6709\u4e0d\u5f53\u4e4b\u5904\uff0c\u8fd8\u8bf7\u8bfb\u8005\u6307\u6b63\uff01<\/p>\n<h2><strong>\u4e00\u3001<\/strong>  <strong>\u4ece\u6570\u636e\u62df\u5408\u8bf4\u8d77<\/strong><\/h2>\n<p>\u5728\u5927\u5b66\u7684\u300a\u6570\u5b66\u5206\u6790\u300b\u3001\u300a\u5fae\u79ef\u5206\u300b\u6216\u8005\u300a\u6570\u503c\u5206\u6790\u300b\u4e2d\uff0c\u5927\u5bb6\u90fd\u5df2\u5b66\u4e60\u5e76\u719f\u6089\u6570\u636e\u62df\u5408\u95ee\u9898\u53ca\u6c42\u89e3\u62df\u5408\u95ee\u9898\u7684\u6700\u5c0f\u4e8c\u4e58\u6cd5\u3002<\/p>\n<p>1.1.      \u6570\u636e\u62df\u5408\u95ee\u9898<\/p>\n<p>\u5728\u79d1\u5b66\u6280\u672f\u7684\u5404\u9886\u57df\u4e2d\uff0c\u6211\u4eec\u6240\u7814\u7a76\u7684\u4e8b\u4ef6\u4e00\u822c\u90fd\u662f\u6709\u89c4\u5f8b\uff08\u56e0\u679c\u5173\u7cfb\uff09\u7684\uff0c\u5373\u81ea\u53d8\u91cf\u96c6\u5408<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image001.png\" alt=\"img\" \/>\u4e0e\u5e94\u53d8\u91cf\u96c6\u5408<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image002.png\" alt=\"img\" \/>\u4e4b\u95f4\u5b58\u5728\u7684\u5bf9\u5e94\u5173\u7cfb\u901a\u5e38\u7528\u6620\u5c04\u6765\u63cf\u8ff0<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/202206201515557.png\" alt=\"img\" \/>\uff08\u7279\u6b8a\u60c5\u51b5\uff1a\u5b9e\u6570\u96c6\u5408<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image004.png\" alt=\"img\" \/>\u5230\u5b9e\u6570\u96c6\u5408<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image004.png\" alt=\"img\" \/>\u4e4b\u95f4\u7684\u6620\u5c04\u79f0\u4e3a\u51fd\u6570\uff09\u3002\u8fd9\u6837\u80fd\u6839\u636e\u6620\u5c04\uff08\u51fd\u6570)\u89c4\u5f8b\u4f5c\u51fa\u9884\u6d4b\u5e76\u7528\u4e8e\u5b9e\u9645\u5e94\u7528\u3002<\/p>\n<p>\u6709\u4e9b\u51fd\u6570\u5173\u7cfb\u53ef\u7531\u7406\u8bba\u5206\u6790\u63a8\u5bfc\u5f97\u51fa\uff0c\u4e0d\u4ec5\u4e3a\u8fdb\u4e00\u6b65\u7684\u5206\u6790\u7814\u7a76\u5de5\u4f5c\u63d0\u4f9b\u7406\u8bba\u57fa\u7840\uff0c\u4e5f\u53ef\u4ee5\u65b9\u4fbf\u7684\u89e3\u51b3\u5b9e\u9645\u5de5\u7a0b\u95ee\u9898\u3002\u6bd4\u5982\uff0c\u9002\u5408\u4e8e\u5b8f\u89c2\u4f4e\u901f\u7269\u4f53\u7684\u725b\u987f\u7b2c\u4e8c\u8fd0\u52a8\u5b9a\u5f8b<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image005.png\" alt=\"img\" \/>\u5c31\u662f\u5728\u5b9e\u9645\u89c2\u5bdf\u548c\u5f52\u7eb3\u4e2d\u5f97\u51fa\u7684\u666e\u9002\u6027\u529b\u5b66\u5b9a\u5f8b\u3002<\/p>\n<p>\u4f46\u662f\uff0c\u5f88\u591a\u5de5\u7a0b\u95ee\u9898\u96be\u4ee5\u76f4\u63a5\u63a8\u5bfc\u51fa\u53d8\u91cf\u4e4b\u95f4\u7684\u51fd\u6570\u8868\u8fbe\u5f0f\uff1b\u6216\u8005\u5373\u4f7f\u80fd\u5f97\u51fa\u8868\u8fbe\u5f0f\uff0c\u516c\u5f0f\u4e5f\u5341\u5206\u590d\u6742\uff0c\u4e0d\u5229\u4e8e\u8fdb\u4e00\u6b65\u7684\u5206\u6790\u4e0e\u8ba1\u7b97\u3002\u8fd9\u65f6\u53ef\u4ee5\u901a\u8fc7\u8bf8\u5982\u91c7\u6837\u3001\u5b9e\u9a8c\u7b49\u65b9\u6cd5\u83b7\u5f97\u82e5\u5e72\u79bb\u6563\u7684\u6570\u636e\uff08\u79f0\u4e3a\u6837\u672c\u6570\u636e\u70b9\uff09\uff0c\u7136\u540e\u6839\u636e\u8fd9\u4e9b\u6570\u636e\uff0c\u5e0c\u671b\u80fd\u5f97\u5230\u8fd9\u4e9b\u53d8\u91cf\u4e4b\u95f4\u7684\u51fd\u6570\u5173\u7cfb\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u79f0\u4e3a\u6570\u636e\u62df\u5408\uff08Data fitting\uff09\uff0c\u5728\u6570\u7406\u7edf\u8ba1\u4e2d\u4e5f\u79f0\u4e3a\u56de\u5f52\u5206\u6790\uff08Regression analysis\uff09\u3002<\/p>\n<p>\u8fd9\u91cc\u503c\u5f97\u63d0\u4e00\u4e0b\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8fd8\u6709\u4e00\u7c7b\u95ee\u9898\u662f\u8f93\u51fa\u7684\u7ed3\u679c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image002.png\" alt=\"img\" \/>\u662f\u79bb\u6563\u578b\u7684\uff08\u6bd4\u5982\u8bc6\u522b\u56fe\u7247\u91cc\u662f\u4eba\u3001\u732b\u3001\u72d7\u7b49\u6807\u7b7e\u7684\u4e00\u79cd\uff09\uff0c\u6b64\u65f6\u95ee\u9898\u79f0\u4e3a\u5206\u7c7b\uff08Classification\uff09\u3002<\/p>\n<p>1.2.      \u6570\u636e\u62df\u5408\u7c7b\u578b<\/p>\n<p>\u6211\u4eec\u5148\u8003\u8651\u6700\u7b80\u5355\u7684\u60c5\u5f62\uff0c\u5373\u5b9e\u6570\u5230\u5b9e\u6570\u7684\u4e00\u5143\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image006.png\" alt=\"img\" \/>\u3002\u5047\u8bbe\u901a\u8fc7\u5b9e\u9a8c\u83b7\u5f97\u4e86<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image007.png\" alt=\"img\" \/>\u4e2a\u6837\u672c\u70b9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image008.png\" alt=\"img\" \/>\u3002\u6211\u4eec\u5e0c\u671b\u6c42\u5f97\u53cd\u6620\u8fd9\u4e9b\u6837\u672c\u70b9\u89c4\u5f8b\u7684\u4e00\u4e2a\u51fd\u6570\u5173\u7cfb<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image009.png\" alt=\"img\" \/>\uff0c\u5982\u56fe1\u6240\u793a\u3002<\/p>\n<p>\u5982\u679c\u8981\u6c42\u51fd\u6570\u4e25\u683c\u901a\u8fc7\u6bcf\u4e2a\u6837\u672c\u70b9\uff0c\u5373<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image010.png\" alt=\"img\" \/> \uff0c<\/th>\n<th>(1.1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<\/tbody>\n<\/table>\n<p>\u5219\u6c42\u89e3\u51fd\u6570\u7684\u95ee\u9898\u79f0\u4e3a<strong>\u63d2\u503c\u95ee\u9898<\/strong>\uff08Interpolation\uff09\u3002<\/p>\n<p><strong>\u4e00\u822c\u5730\uff0c\u7531\u4e8e\u5b9e\u9a8c\u6570\u636e\u5e26\u6709\u89c2\u6d4b\u8bef\u5dee\uff0c\u56e0\u6b64\u5728\u5927\u90e8\u5206\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ea\u8981\u6c42\u51fd\u6570\u53cd\u6620\u8fd9\u4e9b\u6837\u672c\u70b9\u7684\u8d8b\u52bf\uff0c\u5373\u51fd\u6570\u9760\u8fd1\u6837\u672c\u70b9\u4e14\u8bef\u5dee\u5728\u67d0\u79cd\u5ea6\u91cf\u610f\u4e49\u4e0b\u6700\u5c0f\uff0c\u79f0\u4e3a\u903c\u8fd1\u95ee\u9898\uff08Approximation\uff09<\/strong>\u3002\u82e5\u8bb0\u5728\u67d0\u70b9\u7684\u8bef\u5dee\u4e3a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image011.png\" alt=\"img\" \/><\/th>\n<th>(1.2)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<\/tbody>\n<\/table>\n<p>\u4e14\u8bb0\u8bef\u5dee\u5411\u91cf\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image012.png\" alt=\"img\" \/>\u3002\u903c\u8fd1\u95ee\u9898\u5c31\u662f\u8981\u6c42\u5411\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image013.png\" alt=\"img\" \/>\u7684\u67d0\u79cd\u8303\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image014.png\" alt=\"img\" \/>\u6700\u5c0f\u3002\u4e00\u822c\u91c7\u7528\u6b27\u6c0f\u8303\u6570\uff08<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image015.png\" alt=\"img\" \/>\u8303\u6570\uff09\u4f5c\u4e3a\u8bef\u5dee\u5ea6\u91cf\u7684\u6807\u51c6\uff08\u6bd4\u8f83\u5bb9\u6613\u8ba1\u7b97\uff09\uff0c\u5373\u6c42\u5982\u4e0b\u6781\u5c0f\u5316\u95ee\u9898\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image016.png\" alt=\"img\" \/>.<\/th>\n<th>(1.3)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<\/tbody>\n<\/table>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image017.jpg\" alt=\"img\" \/><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image018.jpg\" alt=\"img\" \/><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image019.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe1. \u6570\u636e\u62df\u5408\u3002\u5de6\uff1a\u8f93\u5165\u7684\u6837\u672c\u70b9\uff1b\u4e2d\uff1a\u63d2\u503c\u51fd\u6570\uff1b\u53f3\uff1a\u903c\u8fd1\u51fd\u6570\u3002<\/p>\n<p>\u65e0\u8bba\u662f\u63d2\u503c\u95ee\u9898\u8fd8\u662f\u903c\u8fd1\u95ee\u9898\uff0c\u4e00\u4e2a\u9996\u8981\u7684\u95ee\u9898\u5c31\u662f\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u7684\u7c7b\u578b\u7684\u9009\u62e9\u548c\u8868\u793a\u95ee\u9898\uff0c\u8fd9\u662f\u300a\u51fd\u6570\u903c\u8fd1\u8bba\u300b\u4e2d\u7684\u4e00\u4e2a\u6bd4\u8f83\u201c\u7ea0\u7ed3\u201d\u7684\u95ee\u9898\u3002<\/p>\n<h2><strong>\u4e8c\u3001<\/strong>  <strong>\u51fd\u6570\u903c\u8fd1\u8bba\u7b80\u4ecb<\/strong><\/h2>\n<p>\u51fd\u6570\u7684\u8868\u793a\u662f\u51fd\u6570\u903c\u8fd1\u8bba\u4e2d\u7684\u57fa\u672c\u95ee\u9898\u3002\u5728\u6570\u5b66\u7684\u7406\u8bba\u7814\u7a76\u548c\u5b9e\u9645\u5e94\u7528\u4e2d\u7ecf\u5e38\u9047\u5230\u4e0b\u7c7b\u95ee\u9898\uff1a\u5728\u9009\u5b9a\u7684\u4e00\u7c7b\u51fd\u6570\u4e2d\u5bfb\u627e\u67d0\u4e2a\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\uff0c\u4f7f\u5b83\u4e0e\u5df2\u77e5\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image021.png\" alt=\"img\" \/>\uff08\u6216\u89c2\u6d4b\u6570\u636e\uff09\u5728\u4e00\u5b9a\u610f\u4e49\u4e0b\u4e3a\u6700\u4f73\u8fd1\u4f3c\u8868\u793a\uff0c\u5e76\u6c42\u51fa\u7528<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u8fd1\u4f3c\u8868\u793a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image021.png\" alt=\"img\" \/>\u800c\u4ea7\u751f\u7684\u8bef\u5dee\u3002\u8fd9\u5c31\u662f\u51fd\u6570\u903c\u8fd1\u95ee\u9898\u3002<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u79f0\u4e3a\u903c\u8fd1\u51fd\u6570\u6216\u62df\u5408\u51fd\u6570\u3002<\/p>\n<p>\u5728\u51fd\u6570\u903c\u8fd1\u95ee\u9898\u4e2d\uff0c\u903c\u8fd1\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u7684\u51fd\u6570\u7c7b\u53ef\u4ee5\u6709\u4e0d\u540c\u7684\u9009\u62e9\uff1b\u5373\u4f7f\u51fd\u6570\u7c7b\u9009\u5b9a\u4e86\uff0c\u5728\u8be5\u7c7b\u51fd\u6570\u4e2d\u786e\u5b9a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u7684\u65b9\u5f0f\u4ecd\u7136\u662f\u5404\u5f0f\u5404\u6837\u7684\uff1b<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u5bf9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image021.png\" alt=\"img\" \/>\u7684\u8fd1\u4f3c\u7a0b\u5ea6\uff08\u8bef\u5dee\uff09\u4e5f\u53ef\u4ee5\u6709\u5404\u79cd\u4e0d\u540c\u7684\u5b9a\u4e49\u3002\u6211\u4eec\u5206\u522b\u5bf9\u8fd9\u4e9b\u95ee\u9898\u8fdb\u884c\u7406\u89e3\u548c\u8ba8\u8bba\u3002<\/p>\n<p>2.1.       \u903c\u8fd1\u51fd\u6570\u7c7b<\/p>\n<p>\u5728\u5b9e\u9645\u95ee\u9898\u4e2d\uff0c\u9996\u5148\u8981\u786e\u5b9a\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u7684\u5177\u4f53\u5f62\u5f0f\u3002\u8fd9\u4e0d\u5355\u7eaf\u662f\u6570\u5b66\u95ee\u9898\uff0c\u8fd8\u4e0e\u6240\u7814\u7a76\u95ee\u9898\u7684\u8fd0\u52a8\u89c4\u5f8b\u53ca\u89c2\u6d4b\u6570\u636e\u6709\u5173\uff0c\u4e5f\u4e0e\u7528\u6237\u7684\u7ecf\u9a8c\u6709\u5173\u3002\u4e00\u822c\u5730\uff0c\u6211\u4eec\u5728\u67d0\u4e2a\u8f83\u7b80\u5355\u7684\u51fd\u6570\u7c7b\u4e2d\u53bb\u5bfb\u627e\u6211\u4eec\u6240\u9700\u8981\u7684\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u3002\u8fd9\u79cd\u51fd\u6570\u7c7b\u53eb\u505a\u903c\u8fd1\u51fd\u6570\u7c7b\u3002<\/p>\n<p>\u903c\u8fd1\u51fd\u6570\u7c7b\u53ef\u4ee5\u6709\u591a\u79cd\u9009\u62e9\uff0c\u4e00\u822c\u53ef\u4ee5\u5728\u4e0d\u540c\u7684\u51fd\u6570\u7a7a\u95f4\uff08\u6bd4\u5982\u7531\u4e00\u4e9b\u57fa\u51fd\u6570\u901a\u8fc7\u7ebf\u6027\u7ec4\u5408\u6240\u5f20\u6210\u7684\u51fd\u6570\u7a7a\u95f4\uff09\u4e2d\u8fdb\u884c\u9009\u62e9\u3002\u5982\u4e0b\u662f\u4e00\u4e9b\u5e38\u7528\u7684\u51fd\u6570\u7c7b\u3002<\/p>\n<p>(1)  \u591a\u9879\u5f0f\u51fd\u6570\u7c7b<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u6b21\u4ee3\u6570\u591a\u9879\u5f0f\uff0c\u5373\u7531\u6b21\u6570\u4e0d\u5927\u4e8e<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u7684\u5e42\u57fa<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image023.png\" alt=\"img\" \/>\u7684\u7ebf\u6027\u7ec4\u5408\u7684\u591a\u9879\u5f0f\u51fd\u6570\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image024.png\" alt=\"img\" \/>,<\/th>\n<th>(2.1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image025.png\" alt=\"img\" \/>\u4e3a\u5b9e\u7cfb\u6570\u3002<\/p>\n<p>\u66f4\u5e38\u7528\u7684\u662f\u7531<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u6b21Bernstein\u57fa\u51fd\u6570\u6765\u8868\u8fbe\u7684\u591a\u9879\u5f0f\u5f62\u5f0f\uff08\u79f0\u4e3aBernstein\u591a\u9879\u5f0f\u6216Bezier\u591a\u9879\u5f0f\uff09\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image026.png\" alt=\"img\" \/>,<\/th>\n<th>(2.2)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2dBernstein\u57fa\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image027.png\" alt=\"img\" \/><\/p>\n<p>(2)  \u4e09\u89d2\u591a\u9879\u5f0f\u7c7b<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u9636\u4e09\u89d2\u591a\u9879\u5f0f\uff0c\u5373\u7531\u9636\u6570\u4e0d\u5927\u4e8e<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u7684\u4e09\u89d2\u51fd\u6570\u57fa\u7684\u7ebf\u6027\u7ec4\u5408\u7684\u4e09\u89d2\u51fd\u6570\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image028.png\" alt=\"img\" \/>,<\/th>\n<th>(2.3)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image029.png\" alt=\"img\" \/>\u4e3a\u5b9e\u7cfb\u6570\u3002<\/p>\n<p>\u8fd9\u4e9b\u662f\u5e38\u7528\u7684\u903c\u8fd1\u51fd\u6570\u7c7b\u3002\u5728\u903c\u8fd1\u8bba\u4e2d\uff0c\u8fd8\u6709\u8bb8\u591a\u5176\u4ed6\u5f62\u5f0f\u7684\u903c\u8fd1\u51fd\u6570\u7c7b\uff0c\u6bd4\u5982\u7531\u4ee3\u6570\u591a\u9879\u5f0f\u7684\u6bd4\u6784\u6210\u7684\u6709\u7406\u5206\u5f0f\u96c6\uff08\u6709\u7406\u903c\u8fd1\uff09\uff1b\u6309\u7167\u4e00\u5b9a\u6761\u4ef6\u5b9a\u4e49\u7684\u6837\u6761\u51fd\u6570\u96c6\uff08\u6837\u6761\u903c\u8fd1\uff09\uff1b\u5f84\u5411\u57fa\u51fd\u6570\uff08RBF\u903c\u8fd1\uff09\uff1b\u7531\u6b63\u4ea4\u51fd\u6570\u7cfb\u7684\u7ebf\u6027\u7ec4\u5408\u6784\u6210\u7684\uff08\u7ef4\u6570\u56fa\u5b9a\u7684\uff09\u51fd\u6570\u96c6\u7b49\u3002<\/p>\n<p>2.2.      \u4e07\u80fd\u903c\u8fd1\u5b9a\u7406<\/p>\n<p>\u5728\u51fd\u6570\u903c\u8fd1\u8bba\u4e2d\uff0c\u5982\u679c\u4e00\u7ec4\u51fd\u6570\u6210\u4e3a\u4e00\u7ec4\u201c\u57fa\u201d\u51fd\u6570\uff0c\u9700\u8981\u6ee1\u8db3\u4e00\u4e9b\u6bd4\u8f83\u597d\u7684\u6027\u8d28\uff0c\u6bd4\u5982\u5149\u6ed1\u6027\u3001\u7ebf\u6027\u65e0\u5173\u6027\u3001\u6743\u6027\uff08\u6240\u6709\u57fa\u51fd\u6570\u548c\u4e3a1\uff09\u3001\u5c40\u90e8\u652f\u96c6\u3001\u5b8c\u5907\u6027\u3001\u6b63\u6027\u3001\u51f8\u6027\u7b49\u3002\u5176\u4e2d\uff0c \u201c\u5b8c\u5907\u6027\u201d\u662f\u6307\uff0c\u8be5\u7ec4\u51fd\u6570\u7684\u7ebf\u6027\u7ec4\u5408\u662f\u5426\u80fd\u591f\u4ee5\u4efb\u610f\u7684\u8bef\u5dee\u548c\u7cbe\u5ea6\u6765\u903c\u8fd1\u7ed9\u5b9a\u7684\u51fd\u6570\uff08\u5373\u4e07\u80fd\u903c\u8fd1\u6027\u8d28\uff09\uff1f<\/p>\n<p>\u5bf9\u4e8e\u591a\u9879\u5f0f\u51fd\u6570\u7c7b\uff0c\u6211\u4eec\u6709\u4ee5\u4e0b\u7684\u201c\u4e07\u80fd\u903c\u8fd1\u5b9a\u7406\u201d\uff1a<\/p>\n<p><strong>\u3010\u5b9a\u74062.1\uff08Weierstrass\u903c\u8fd1\u5b9a\u7406\uff09\u3011<\/strong>\u5bf9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image030.png\" alt=\"img\" \/>\u4e0a\u7684\u4efb\u610f\u8fde\u7eed\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image021.png\" alt=\"img\" \/>\uff0c\u53ca\u4efb\u610f\u7ed9\u5b9a\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image031.png\" alt=\"img\" \/>\uff0c\u5fc5\u5b58\u5728<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u6b21\u4ee3\u6570\u591a\u9879\u5f0f<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image024.png\" alt=\"img\" \/>\uff0c\u4f7f\u5f97<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image032.png\" alt=\"img\" \/><\/th>\n<th>(2.4)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Weierstrass\u903c\u8fd1\u5b9a\u7406\u8868\u660e\uff0c\u53ea\u8981\u6b21\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u8db3\u591f\u9ad8\uff0c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u6b21\u591a\u9879\u5f0f\u5c31\u80fd\u4ee5\u4efb\u4f55\u7cbe\u5ea6\u903c\u8fd1\u7ed9\u5b9a\u7684\u51fd\u6570\u3002\u5177\u4f53\u7684\u6784\u9020\u65b9\u6cd5\u6709Bernstein\u591a\u9879\u5f0f\u6216Chebyshev\u591a\u9879\u5f0f\u7b49\uff0c\u8fd9\u91cc\u4e0d\u8be6\u7ec6\u5c55\u5f00\u3002<\/p>\n<p>\u7c7b\u4f3c\u5730\uff0c\u7531Fourier\u5206\u6790\u7406\u8bba\uff08\u6216Weierstrass\u7b2c\u4e8c\u903c\u8fd1\u5b9a\u7406\uff09\uff0c\u53ea\u8981\u9636\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u8db3\u591f\u9ad8\uff0c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u9636\u4e09\u89d2\u51fd\u6570\u5c31\u80fd\u4ee5\u4efb\u4f55\u7cbe\u5ea6\u903c\u8fd1\u7ed9\u5b9a\u7684\u5468\u671f\u51fd\u6570\u3002\u8fd9\u4e9b\u7406\u8bba\u8868\u660e\uff0c\u591a\u9879\u5f0f\u51fd\u6570\u7c7b\u548c\u4e09\u89d2\u51fd\u6570\u7c7b\u5728\u51fd\u6570\u7a7a\u95f4\u662f\u201c\u7a20\u5bc6\u201d\u7684\uff0c\u8fd9\u5c31\u4fdd\u969c\u4e86\u7528\u8fd9\u4e9b\u51fd\u6570\u7c7b\u6765\u4f5c\u4e3a\u903c\u8fd1\u51fd\u6570\u662f\u201c\u5408\u7406\u201d\u7684\u3002<\/p>\n<p>2.3.      \u903c\u8fd1\u51fd\u6570\u7c7b\u9009\u62e9\u7684\u201c\u7ea0\u7ed3\u201d<\/p>\n<p>\u5728\u4e00\u4e2a\u903c\u8fd1\u95ee\u9898\u4e2d\u9009\u62e9\u4ec0\u4e48\u6837\u7684\u51fd\u6570\u7c7b\u4f5c\u903c\u8fd1\u51fd\u6570\u7c7b\uff0c\u8fd9\u8981\u53d6\u51b3\u4e8e\u88ab\u903c\u8fd1\u51fd\u6570\u672c\u8eab\u7684\u7279\u70b9\uff0c\u4e5f\u548c\u903c\u8fd1\u95ee\u9898\u7684\u6761\u4ef6\u3001\u8981\u6c42\u7b49\u56e0\u7d20\u6709\u5173\u3002<\/p>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8fd9\u91cc\u5176\u5b9e\u5b58\u5728\u7740\u4e24\u4e2a\u975e\u5e38\u201c\u7ea0\u7ed3\u201d\u7684\u95ee\u9898\u3002<\/p>\n<p>\u7b2c\u4e00\uff0c\u9009\u62e9\u4ec0\u4e48\u6837\u7684\u903c\u8fd1\u51fd\u6570\u7c7b\uff1f\u4e00\u822c\u5730\uff0c\u9700\u8981\u7528\u6237\u5bf9\u88ab\u903c\u8fd1\u5bf9\u8c61\u6216\u6837\u672c\u6570\u636e\u6709\u4e00\u4e9b\u201c\u5148\u9a8c\u77e5\u8bc6\u201d\u6765\u51b3\u5b9a\u9009\u62e9\u5177\u4f53\u7684\u903c\u8fd1\u51fd\u6570\u7c7b\u3002\u6bd4\u5982\uff0c\u5982\u679c\u88ab\u903c\u8fd1\u7684\u51fd\u6570\u5177\u6709\u5468\u671f\u6027\uff0c\u5c06\u4e09\u89d2\u51fd\u6570\u4f5c\u4e3a\u903c\u8fd1\u51fd\u6570\u662f\u4e2a\u5408\u7406\u7684\u9009\u62e9\uff1b\u5982\u679c\u88ab\u903c\u8fd1\u7684\u51fd\u6570\u5177\u6709\u5947\u70b9\uff0c\u5c06\u6709\u7406\u51fd\u6570\u4f5c\u4e3a\u903c\u8fd1\u51fd\u6570\u66f4\u4e3a\u5408\u7406\uff0c\u7b49\u7b49\u3002<\/p>\n<p>\u7b2c\u4e8c\uff0c\u5373\u4f7f\u786e\u5b9a\u4e86\u903c\u8fd1\u51fd\u6570\u7c7b\uff0c\u9009\u62e9\u591a\u9ad8\u7684\u6b21\u6570\u6216\u9636\u6570\uff1f\u6bd4\u5982\uff0c\u5982\u679c\u9009\u62e9\u4e86\u591a\u9879\u5f0f\u51fd\u6570\u7c7b\uff0c\u6839\u636eLagrange\u63d2\u503c\u5b9a\u7406\uff0c\u4e00\u5b9a\u80fd\u627e\u5230\u4e00\u4e2a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image033.png\" alt=\"img\" \/>\u6b21\u591a\u9879\u5f0f\u6765\u63d2\u503c\u7ed9\u5b9a\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u4e2a\u6837\u672c\u70b9\u3002\u4f46\u5982\u679c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u8f83\u5927\uff0c\u5219\u8fd9\u6837\u5f97\u5230\u7684\u9ad8\u6b21\u591a\u9879\u5f0f\u5f88\u5bb9\u6613\u9020\u6210\u201c\u8fc7\u62df\u5408\u201d\uff08Overfitting\uff09\u3002\u800c\u5982\u679c\u9009\u62e9\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u8fc7\u5c0f\uff0c\u5219\u5f97\u5230\u7684\u591a\u9879\u5f0f\u5bb9\u6613\u9020\u6210\u201c\u6b20\u62df\u5408\u201d\uff08Underfitting\uff09\u3002\u5982\u56fe2\u6240\u793a\u3002\u8fc7\u62df\u5408\u6216\u6b20\u62df\u5408\u51fd\u6570\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u662f\u6ca1\u6709\u7528\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u9884\u6d4b\u80fd\u529b\u975e\u5e38\u5dee\uff01<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image034.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe2. \u7528\u4e0d\u540c\u6b21\u6570\u7684\u591a\u9879\u5f0f\u62df\u5408\u6837\u672c\u70b9\uff08\u84dd\u8272\u70b9\uff09\u3002<\/p>\n<p>\u5de6\uff1a\u6b20\u62df\u5408\uff1b\u4e2d\uff1a\u5408\u9002\u7684\u62df\u5408\uff1b\u53f3\uff1a\u8fc7\u62df\u5408\u3002<\/p>\n<p>\u8fd9\u91cc\u6709\u4e2a\u6982\u5ff5\u9700\u8981\u63d0\u53ca\u4e00\u4e0b\u3002\u4e00\u4e2a\u903c\u8fd1\u51fd\u6570\u201c\u8868\u8fbe\u80fd\u529b\u201d\u4f53\u73b0\u5728\u8be5\u51fd\u6570\u7684\u672a\u77e5\u53c2\u6570\uff08\u5373\u516c\u5f0f(2.1)-(2.3)\u4e2d\u7684\u7cfb\u6570\uff09\u4e0e\u6837\u672c\u70b9\u4e2a\u6570\u7684\u5dee\uff0c\u4e5f\u79f0\u4e3a\u201c\u81ea\u7531\u5ea6\u201d\u3002\u5982\u679c\u903c\u8fd1\u51fd\u6570\u7684\u672a\u77e5\u53c2\u6570\u8d8a\u591a\uff0c\u5219\u8868\u8fbe\u80fd\u529b\u8d8a\u5f3a\u3002\u7136\u800c\uff0c\u5728\u5b9e\u9645\u7684\u62df\u5408\u95ee\u9898\u4e2d\uff0c\u903c\u8fd1\u51fd\u6570\u7684\u62df\u5408\u80fd\u529b\u5e76\u975e\u8d8a\u5f3a\u8d8a\u597d\u3002\u56e0\u4e3a\u5982\u679c\u53ea\u5173\u6ce8\u6837\u672c\u70b9\u5904\u7684\u62df\u5408\u8bef\u5dee\u7684\u8bdd\uff0c\u975e\u5e38\u5f3a\u7684\u8868\u8fbe\u80fd\u529b\u4f1a\u4f7f\u5f97\u6837\u672c\u70b9\u4e4b\u5916\u7684\u51fd\u6570\u503c\u8fdc\u8fdc\u504f\u79bb\u671f\u671b\u7684\u76ee\u6807\uff0c\u53cd\u800c\u964d\u4f4e\u62df\u5408\u51fd\u6570\u7684\u9884\u6d4b\u6027\u80fd\uff0c\u4ea7\u751f\u8fc7\u62df\u5408\uff0c\u5982\u56fe2 (\u53f3)\u6240\u793a\u3002<\/p>\n<p>\u4eba\u4eec\u53d1\u5c55\u51fa\u5404\u79cd\u65b9\u6cd5\u6765\u51cf\u7f13\uff08\u4e0d\u80fd\u5b8c\u5168\u907f\u514d\uff09\u8fc7\u62df\u5408\u3002\u6bd4\u5982\uff0c\u5254\u9664\u6837\u672c\u70b9\u4e2d\u7684\u566a\u58f0\uff08\u6570\u636e\u53bb\u566a\uff09\u3001\u589e\u52a0\u6837\u672c\u70b9\u6570\u636e\u91cf\uff08\u6570\u636e\u589e\u5e7f\uff09\u3001\u7b80\u5316\u9884\u6d4b\u6a21\u578b\u3001\u83b7\u53d6\u989d\u5916\u6570\u636e\u8fdb\u884c\u4ea4\u53c9\u9a8c\u8bc1\u3001\u6216\u5bf9\u76ee\u6807\u51fd\u6570\u8fdb\u884c\u9002\u5f53\u7684\u6b63\u5219\u5316\u7b49\u3002\u5728\u6b64\u4e0d\u8be6\u7ec6\u53d9\u8ff0\u3002<\/p>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u4f55\u9009\u62e9\u62df\u5408\u51fd\u6570\u7684\u6570\u5b66\u6a21\u578b\uff08\u5408\u9002\u7684\u903c\u8fd1\u51fd\u6570\u7c7b\u53ca\u5176\u9636\u6570\uff09\uff0c\u5e76\u4e0d\u662f\u4e00\u5f00\u59cb\u5c31\u80fd\u9009\u597d\uff0c\u5f80\u5f80\u987b\u901a\u8fc7\u5206\u6790\u786e\u5b9a\u82e5\u5e72\u6a21\u578b\u540e\uff0c\u518d\u7ecf\u8fc7\u5b9e\u9645\u8ba1\u7b97\u3001\u6bd4\u8f83\u548c\u8c03\u6574\u624d\u80fd\u9009\u5230\u8f83\u597d\u7684\u6a21\u578b\u3002\u9700\u8981\u4e0d\u65ad\u7684\u8bd5\u9a8c\u548c\u8c03\u8bd5\uff08\u79f0\u4e3a\u201c\u8c03\u53c2\u201d\u8fc7\u7a0b\uff09\uff0c\u662f\u4e2a\u9700\u8981\u4e30\u5bcc\u7ecf\u9a8c\u7684\u201c\u6280\u672f\u6d3b\u201d\u3002<\/p>\n<p>2.4.      \u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08Least Squares Method\uff09<\/p>\n<p>\u5047\u8bbe\u901a\u8fc7\u5206\u6790\u6211\u4eec\u5df2\u7ecf\u786e\u5b9a\u4e86\u903c\u8fd1\u51fd\u6570\u7c7b\u53ca\u5176\u6b21\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u3002\u8bb0\u57fa\u51fd\u6570\uff08\u4e00\u822c\u7ebf\u6027\u65e0\u5173\uff09\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image035.png\" alt=\"img\" \/>\u3002\u8bb0<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image036.png\" alt=\"img\" \/>\u4e3a\u8fd9\u4e9b\u57fa\u51fd\u6570\u6240\u5f20\u6210\u7684\u7ebf\u6027\u7a7a\u95f4\uff08\u51fd\u6570\u7a7a\u95f4\uff09\u3002\u5219\u903c\u8fd1\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u53ef\u8bb0\u4e3a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image037.png\" alt=\"img\" \/>,<\/th>\n<th>(2.5)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image038.png\" alt=\"img\" \/>\u4e3a\u5f85\u5b9a\u6743\u7cfb\u6570\u3002<\/p>\n<p>\u5173\u4e8e\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u4e00\u822c\u63d0\u6cd5\u662f\uff1a\u5bf9\u7ed9\u5b9a\u7684\u4e00\u7ec4\u6837\u672c\u70b9\u6570\u636e<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image039.png\" alt=\"img\" \/>\uff0c\u8981\u6c42\u5728\u51fd\u6570\u7c7b<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image040.png\" alt=\"img\" \/>\u4e2d\u627e\u4e00\u4e2a\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\uff0c\u4f7f\u8bef\u5dee\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image015.png\" alt=\"img\" \/>\u6a21\u7684\u5e73\u65b9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image041.png\" alt=\"img\" \/>\uff0c\u5373\u5f0f(1.3)\uff0c\u8fbe\u5230\u6700\u5c0f\u3002<\/p>\n<p>\u5bf9\u4e8e\u5206\u6790\u6781\u5c0f\u5316\u8bef\u5dee(1.3)\uff0c\u53ef\u5f97\u5173\u4e8e\u7cfb\u6570\u5411\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image042.png\" alt=\"img\" \/>\u7684\u6cd5\u65b9\u7a0b<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image043.png\" alt=\"img\" \/>,<\/th>\n<th>(2.6)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4ece\u800c\u53ef\u6c42\u5f97<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image044.png\" alt=\"img\" \/>.<\/th>\n<th>(2.7)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u7531\u4e8e\u6cd5\u65b9\u7a0b\u662f\u4e00\u4e2a\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u56e0\u6b64\u57fa\u4e8e\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u51fd\u6570\u6c42\u89e3\u4e5f\u79f0\u4e3a\u7ebf\u6027\u56de\u5f52\u3002<\/p>\n<p>\u53e6\u5916\uff0c\u6211\u4eec\u53ef\u5728\u8bef\u5dee\u9879\u4e2d\u52a0\u4e2a\u6743\uff0c\u8868\u793a\u4e0d\u540c\u70b9\u5904\u7684\u6570\u636e\u6bd4\u91cd\u4e0d\u540c\uff0c\u6b64\u65f6\u79f0\u4e3a\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u65b9\u6cd5\uff08Weighted least squares, WLS\uff09\u3002\u53e6\u5916\uff0c\u8fd8\u6709\u79fb\u52a8\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08Moving least squares, MLS\uff09\u7b49\u5176\u4ed6\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u6539\u8fdb\u65b9\u6cd5\u3002\u6b64\u5904\u4e0d\u8be6\u7ec6\u53d9\u8ff0\u3002<\/p>\n<h2><strong>\u4e09\u3001<\/strong>  <strong>\u7a00\u758f\u8868\u8fbe\u548c\u7a00\u758f\u5b66\u4e60<\/strong><\/h2>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c 2.3\u8282\u4e2d\u6240\u8ff0\u7684\u4e24\u4e2a\u201c\u7ea0\u7ed3\u201d\u95ee\u9898\u65f6\u6709\u53d1\u751f\u3002\u4eba\u4eec\u53d1\u5c55\u51fa\u4e0d\u540c\u7684\u65b9\u6cd5\u6765\u5c1d\u8bd5\u89e3\u51b3\u3002<\/p>\n<p>3.1.      \u5cad\u56de\u5f52\uff08Ridge Regression\uff09<\/p>\n<p>\u5f53\u6570\u636e\u91cf\u8f83\u5c11\u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08\u7ebf\u6027\u56de\u5f52\uff09\u5bb9\u6613\u51fa\u73b0\u8fc7\u62df\u5408\u7684\u73b0\u8c61\uff0c\u6cd5\u65b9\u7a0b\u7684\u7cfb\u6570\u77e9\u9635<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image045.png\" alt=\"img\" \/>\u4f1a\u51fa\u73b0\u5947\u5f02\uff08\u975e\u6ee1\u79e9\uff09\uff0c\u6b64\u65f6\u56de\u5f52\u7cfb\u6570\u4f1a\u53d8\u5f97\u5f88\u5927\uff0c\u65e0\u6cd5\u6c42\u89e3\u3002<\/p>\n<p>\u8fd9\u65f6\u5728\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u7ed3\u679c\uff08\u5f0f(2.7)\uff09\u4e2d\u52a0\u4e00\u4e2a\u5c0f\u6270\u52a8<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image046.png\" alt=\"img\" \/>\uff0c\u4f7f\u539f\u5148\u65e0\u6cd5\u6c42\u5e7f\u4e49\u9006\u7684\u60c5\u51b5\u53d8\u6210\u53ef\u4ee5\u6c42\u51fa\u5176\u5e7f\u4e49\u9006\uff0c\u4f7f\u5f97\u95ee\u9898\u7a33\u5b9a\u5e76\u5f97\u4ee5\u6c42\u89e3\uff0c\u5373<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image047.png\" alt=\"img\" \/>.<\/th>\n<th>(3.1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e2a\u89e3\u5bf9\u5e94\u4e8e\u5982\u4e0b\u6781\u5c0f\u5316\u95ee\u9898\u7684\u89e3\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image048.png\" alt=\"img\" \/>.<\/th>\n<th>(3.2)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image049.png\" alt=\"img\" \/>\uff0c\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image050.png\" alt=\"img\" \/>\u79f0\u4e3a\u6b63\u5219\u5316\u53c2\u6570\uff08\u5cad\u53c2\u6570\uff09\u3002\u4e0a\u8ff0\u56de\u5f52\u6a21\u578b\u79f0\u4e3a\u5cad\u56de\u5f52\uff0c\u5176\u4e0e\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u533a\u522b\u5728\u4e8e\u591a\u4e86\u5173\u4e8e\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image051.png\" alt=\"img\" \/>\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image015.png\" alt=\"img\" \/>\u8303\u6570\u6b63\u5219\u9879\u3002\u8fd9\u4e00\u9879\u662f\u5bf9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image051.png\" alt=\"img\" \/>\u7684\u5404\u4e2a\u5143\u7d20\u7684\u603b\u4f53\u7684\u5e73\u8861\u7a0b\u5ea6\uff0c\u5373\u9650\u5236\u8fd9\u4e9b\u6743\u7a00\u758f\u7684\u65b9\u5dee\u4e0d\u80fd\u592a\u5927\u3002<\/p>\n<p>\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u679c\u5cad\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image050.png\" alt=\"img\" \/>\u9009\u53d6\u8fc7\u5927\uff0c\u4f1a\u628a\u6240\u6709\u7cfb\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image051.png\" alt=\"img\" \/>\u5747\u6700\u5c0f\u5316\uff08\u8d8b\u5411\u4e8e0\uff09\uff0c\u9020\u6210\u6b20\u62df\u5408\uff1b\u5982\u679c\u5cad\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image050.png\" alt=\"img\" \/>\u9009\u53d6\u8fc7\u5c0f\uff0c\u4f1a\u5bfc\u81f4\u5bf9\u8fc7\u62df\u5408\u95ee\u9898\u89e3\u51b3\u4e0d\u5f53\u3002\u56e0\u6b64\u5cad\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image050.png\" alt=\"img\" \/>\u7684\u9009\u53d6\u4e5f\u662f\u4e00\u4e2a\u6280\u672f\u6d3b\uff0c\u9700\u8981\u4e0d\u65ad\u8c03\u53c2\u3002\u5bf9\u4e8e\u67d0\u4e9b\u60c5\u5f62\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u5206\u6790\u9009\u62e9\u4e00\u4e2a\u6700\u4f73\u7684\u5cad\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image050.png\" alt=\"img\" \/>\u6765\u4fdd\u8bc1\u56de\u5f52\u7684\u6548\u679c\uff0c\u5728\u6b64\u4e0d\u8be6\u7ec6\u53d9\u8ff0\u3002<\/p>\n<p>3.2.      Lasso\u56de\u5f52\uff08Least Absolute Shrinkage and Selection Operator\uff09<\/p>\n<p>Lasso\u56de\u5f52\u7684\u6781\u5c0f\u5316\u95ee\u9898\u4e3a\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image052.png\" alt=\"img\" \/>,<\/th>\n<th>(3.3)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image053.png\" alt=\"img\" \/>\uff0c\u6b63\u5219\u9879\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image054.png\" alt=\"img\" \/>\u8303\u6570\u6b63\u5219\u9879\u3002Lasso\u56de\u5f52\u80fd\u591f\u4f7f\u5f97\u7cfb\u6570\u5411\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image051.png\" alt=\"img\" \/>\u7684\u4e00\u4e9b\u5143\u7d20\u53d8\u4e3a0\uff08\u7a00\u758f\uff09\uff0c\u56e0\u6b64\u5f97\u5230\u7684\u62df\u5408\u51fd\u6570\u4e3a\u90e8\u5206\u57fa\u51fd\u6570\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<p>3.3.      \u7a00\u758f\u8868\u8fbe\u4e0e\u7a00\u758f\u5b66\u4e60<\/p>\n<p>\u6839\u636eLasso\u56de\u5f52\u7684\u5206\u6790\uff0c\u6211\u4eec\u53ef\u901a\u8fc7\u5bf9\u56de\u5f52\u53d8\u91cf\u65bd\u52a0<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image055.png\" alt=\"img\" \/>\u8303\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image056.png\" alt=\"img\" \/>\uff08<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image055.png\" alt=\"img\" \/>\u8303\u6570\u4e3a\u5143\u7d20\u4e2d\u975e0\u5143\u7d20\u7684\u4e2a\u6570\uff0c\u5728\u5f88\u591a\u65f6\u5019\u53ef\u4ee5\u7528<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image054.png\" alt=\"img\" \/>\u8303\u6570\u8fd1\u4f3c\uff09\u7684\u6b63\u5219\u9879\uff0c\u4ee5\u8fbe\u5230\u5bf9\u56de\u5f52\u53d8\u91cf\u8fdb\u884c\u7a00\u758f\u5316\uff0c\u5373\u5927\u90e8\u5206\u56de\u5f52\u53d8\u91cf\u4e3a0\uff08\u5c11\u6570\u56de\u5f52\u53d8\u91cf\u975e0\uff09\u3002\u8fd9\u79cd\u4f18\u5316\u79f0\u4e3a\u7a00\u758f\u4f18\u5316\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u56de\u5f52\u53d8\u91cf\u65bd\u52a0<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image054.png\" alt=\"img\" \/>\u8303\u6570\u80fd\u591f\u201c\u81ea\u52a8\u201d\u5bf9\u57fa\u51fd\u6570\u8fdb\u884c\u9009\u62e9\uff0c\u503c\u4e3a0\u7684\u7cfb\u6570\u6240\u5bf9\u5e94\u7684\u57fa\u51fd\u6570\u5bf9\u6700\u540e\u7684\u903c\u8fd1\u65e0\u8d21\u732e\u3002\u8fd9\u4e9b\u975e0\u7684\u57fa\u51fd\u6570\u53cd\u6620\u4e86\u7684\u6837\u672c\u70b9\u96c6\u5408\u7684\u201c\u7279\u5f81\u201d\uff0c\u56e0\u6b64\u4e5f\u79f0\u4e3a\u7279\u5f81\u9009\u62e9\u3002<\/p>\n<p>\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u9632\u6b62\u4e22\u5931\u4e00\u4e9b\u57fa\u51fd\u6570\uff08\u7279\u5f81\uff09\uff0c\u6211\u4eec\u5f80\u5f80\u53ef\u4ee5\u591a\u9009\u53d6\u4e00\u4e9b\u57fa\u51fd\u6570\uff08\u751a\u81f3\u53ef\u4ee5\u662f\u7ebf\u6027\u76f8\u5173\u7684\uff09\uff0c\u4f7f\u5f97\u57fa\u51fd\u6570\u7684\u4e2a\u6570\u6bd4\u8f93\u5165\u5411\u91cf\u7684\u7ef4\u6570\u8fd8\u8981\u5927\uff0c\u79f0\u4e3a\u201c\u8d85\u5b8c\u5907\u201d\u57fa\uff08Over-complete basis\uff09\u6216\u8fc7\u5197\u4f59\u57fa\uff0c\u5728\u7a00\u758f\u5b66\u4e60\u4e2d\u4ea6\u79f0\u4e3a\u201c\u5b57\u5178\u201d\u3002\u7136\u540e\u901a\u8fc7\u5bf9\u57fa\u51fd\u6570\u7684\u7cfb\u6570\u8fdb\u884c\u7a00\u758f\u4f18\u5316\uff0c\u9009\u62e9\u51fa\u5408\u9002\uff08\u975e0\u7cfb\u6570\uff09\u7684\u57fa\u51fd\u6570\u7684\u7ec4\u5408\u6765\u8868\u8fbe\u903c\u8fd1\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u3002<\/p>\n<p>\u8fd9\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u514b\u670d\u4e862.3\u8282\u4e2d\u6240\u63d0\u51fa\u7684\u4e24\u4e2a\u201c\u7ea0\u7ed3\u201d\u7684\u95ee\u9898\u3002\u56e0\u4e3a\uff0c\u8fd9\u65f6\u53ef\u4ee5\u9009\u53d6\u8f83\u591a\u7684\u57fa\u51fd\u6570\u53ca\u8f83\u9ad8\u7684\u6b21\u6570\uff0c\u901a\u8fc7\u7a00\u758f\u4f18\u5316\u6765\u9009\u62e9\uff08\u201c\u5b66\u4e60\u201d\uff09\u5408\u9002\u7684\u57fa\u5143\u51fd\u6570\uff0c\u4e5f\u79f0\u4e3a\u7a00\u758f\u5b66\u4e60\u3002\u53e6\u5916\uff0c\u57fa\u51fd\u6570\uff08\u5b57\u5178\uff09\u548c\u7a00\u758f\u7cfb\u6570\u4e5f\u53ef\u4ee5\u540c\u65f6\u901a\u8fc7\u4f18\u5316\u5b66\u4e60\u5f97\u5230\uff0c\u79f0\u4e3a\u5b57\u5178\u5b66\u4e60\u3002<\/p>\n<p>\u5bf9\u4e8e\u77e9\u9635\u5f62\u5f0f\uff08\u6bd4\u5982\u591a\u5143\u51fd\u6570\u6216\u56fe\u50cf\uff09\uff0c\u77e9\u9635\u7684\u7a00\u758f\u8868\u73b0\u4e3a\u77e9\u9635\u7684\u4f4e\u79e9\uff08\u8fd1\u4f3c\u4e3a\u6838\u6a21\u5f88\u5c0f\uff09\uff0c\u5219\u5bf9\u5e94\u7740\u77e9\u9635\u4f4e\u79e9\u6c42\u89e3\u95ee\u9898\u3002\u5728\u6b64\u4e0d\u8be6\u7ec6\u53d9\u8ff0\u3002<\/p>\n<p>\u7a00\u758f\u5b66\u4e60\u4e0e\u6700\u8fd1\u5341\u5e74\u6765\u6d41\u884c\u7684\u538b\u7f29\u611f\u77e5\uff08Compressive sensing\uff09\u7406\u8bba\u4e0e\u65b9\u6cd5\u975e\u5e38\u76f8\u5173\uff0c\u4e5f\u662f\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u4e00\u79cd\u91cd\u8981\u65b9\u6cd5\u3002\u5176\u6df1\u539a\u7684\u7406\u8bba\u57fa\u7840\u7531\u534e\u88d4\u6570\u5b66\u5bb6\u9676\u54f2\u8f69\uff082006\u5e74\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u83f2\u5c14\u5179\u5956\u5f97\u4e3b\uff09\u3001\u65af\u5766\u798f\u5927\u5b66\u7edf\u8ba1\u5b66\u6559\u6388David Donoho\uff082018\u5e74\u56fd\u9645\u6570\u5b66\u5bb6\u5927\u4f1a\u9ad8\u65af\u5956\u5f97\u4e3b\uff09\u7b49\u4eba\u6240\u5efa\u7acb\uff0c\u5df2\u6210\u529f\u7528\u4e8e\u4fe1\u53f7\u5904\u7406\u3001\u56fe\u50cf\u4e0e\u89c6\u9891\u5904\u7406\u3001\u8bed\u97f3\u5904\u7406\u7b49\u9886\u57df\u3002\u5728\u6b64\u4e0d\u8be6\u7ec6\u5c55\u5f00\u4ecb\u7ecd\u3002<\/p>\n<p>\u8fd1\u5e74\u6765\uff0c\u7b14\u8005\u53ca\u5176\u56e2\u961f\u6210\u529f\u5730\u5c06\u7a00\u758f\u5b66\u4e60\u7684\u7406\u8bba\u548c\u65b9\u6cd5\u63a8\u5e7f\u7528\u4e8e\u4e09\u7ef4\u51e0\u4f55\u5efa\u6a21\u4e0e\u5904\u7406\u4e2d\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u9886\u57df\u5df2\u53d1\u8868\u5341\u4f59\u7bc7\u76f8\u5173\u8bba\u6587\uff08\u5305\u62ec\u5728\u9876\u7ea7\u671f\u520aACM Transactions on Graphics\u4e0a\u53d1\u8868\u4e864\u7bc7\u8bba\u6587\uff09\u3002\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u8be6\u7ec6\u67e5\u770b<a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/\">\u7b14\u8005\u7684\u76f8\u5173\u8bba\u6587<\/a>\uff1a<\/p>\n<p>[3-1] Xu et al. Survey on Sparsity in Geometry Modeling and Processing. Graphical Models, 82, 160-180, 2015. \uff08\u4e09\u7ef4\u51e0\u4f55\u5904\u7406\u7684\u7a00\u758f\u4f18\u5316\u65b9\u6cd5\u7684\u7efc\u8ff0\u8bba\u6587\uff09<\/p>\n<p>[3-2] Wang et al. Construction of Manifolds via Compatible Sparse Representations. ACM Transactions on Graphics, 35(2), Article 14: 1-10, 2016. \uff08\u57fa\u4e8e\u57fa\u51fd\u6570\u7a00\u758f\u9009\u62e9\u7684\u66f2\u9762\u751f\u6210\uff09<\/p>\n<p>[3-3] Xiong et al. Robust Surface Reconstruction via Dictionary Learning. ACM Transactions on Graphics (Proc. Siggraph Asia), 33(6), Article 1: 1-12, 2014. \uff08\u57fa\u4e8e\u5b57\u5178\u5b66\u4e60\u7684\u66f2\u9762\u91cd\u5efa\uff09<\/p>\n<p>[3-4] Zhang et al. Local Barycentric Coordinates. ACM Transactions on Graphics (Proc. Siggraph Asia), 33(6), Article 1: 1-12, 2014. \uff08\u57fa\u4e8e\u7a00\u758f\u4f18\u5316\u7684\u5c40\u90e8\u91cd\u5fc3\u5750\u6807\uff09<\/p>\n<p>[3-5] Hu et al. Co-Segmentation of 3D Shapes via Subspace Clustering. Computer Graphics Forum (Proc. Symposium on Geometry Processing), 31(5): 1703-1713, 2012. \uff08\u57fa\u4e8e\u7279\u5f81\u7a00\u758f\u9009\u62e9\u7684\u4e09\u7ef4\u5f62\u72b6\u5171\u540c\u5206\u5272\uff09<\/p>\n<p>[3-6] Jin et al. Unsupervised Upright Orientation of Man-Made Models. Graphical Models (Proc. GMP), 74(4): 99-108, 2012. \uff08\u57fa\u4e8e\u77e9\u9635\u4f4e\u79e9\u4f18\u5316\u7684\u4e09\u7ef4\u5f62\u72b6\u6b63\u5411\u8ba1\u7b97\uff09<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image057.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe3. \u7a00\u758f\u5b66\u4e60\u65b9\u6cd5\u7528\u4e8e\u4e09\u7ef4\u51e0\u4f55\u7684\u5efa\u6a21\u4e0e\u5904\u7406\uff08\u7b14\u8005\u7684\u5de5\u4f5c\uff09\u3002<\/p>\n<h2><strong>\u56db\u3001<\/strong>  <strong>\u9ad8\u7ef4\u7684\u903c\u8fd1\u51fd\u6570<\/strong><\/h2>\n<p>\u4e0a\u9762\u8ba8\u8bba\u4e86\u6620\u5c04<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image003.png\" alt=\"img\" \/>\u4e3a\u4e00\u5143\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image006.png\" alt=\"img\" \/>\u7684\u60c5\u5f62\u3002\u4e0a\u8ff0\u7684\u6709\u5173\u6982\u5ff5\u548c\u65b9\u6cd5\u540c\u6837\u53ef\u4ee5\u63a8\u5e7f\u81f3\u591a\u5143\u51fd\u6570\uff08<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image058.png\" alt=\"img\" \/>\uff09\u53ca\u5411\u91cf\u503c\u51fd\u6570\uff08<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image059.png\" alt=\"img\" \/>\uff09\u7684\u60c5\u5f62\uff08\u5982\u56fe4\uff09\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image060.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe4. \u4e0d\u540c\u60c5\u5f62\uff08\u7ef4\u6570\uff09\u7684\u903c\u8fd1\u51fd\u6570\u3002<\/p>\n<p>\u5de6\u4e0a\uff1a\u4e00\u5143\u51fd\u6570\uff1b\u53f3\u4e0a\uff1a\u591a\u5143\u51fd\u6570\uff1b\u5de6\u4e0b\uff1a\u4e00\u5143\u5411\u91cf\u503c\u51fd\u6570\uff1b\u53f3\u4e0b\uff1a\u591a\u5143\u5411\u91cf\u503c\u51fd\u6570\u3002<\/p>\n<p>4.1.      \u591a\u5143\u51fd\u6570<\/p>\n<p>\u5047\u8bbe\u6709\u591a\u5143\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image061.png\" alt=\"img\" \/>\uff0c\u5373<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image062.png\" alt=\"img\" \/>\uff0c\u7684\u4e00\u7ec4\u6d4b\u91cf\u6837\u672c\u6570\u636e<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image063.png\" alt=\"img\" \/>\u3002\u8bbe<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image064.png\" alt=\"img\" \/>\u4e2d\u7684\u4e00\u7ec4\u57fa\u51fd\u6570\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image065.png\" alt=\"img\" \/>\u3002\u8981\u6c42\u51fd\u6570<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image066.png\" alt=\"img\" \/>,<\/th>\n<th>(4.1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4f7f\u5f97\u8bef\u5dee<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image067.png\" alt=\"img\" \/><\/th>\n<th>(4.2)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u7684\u5e73\u65b9\u548c\u6700\u5c0f\u3002\u8fd9\u4e0e\u5f0f(1.3)\u548c2.4\u8282\u7684\u6781\u503c\u95ee\u9898\u5b8c\u5168\u4e00\u6837\u3002\u7cfb\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image068.png\" alt=\"img\" \/>, \u540c\u6837\u901a\u8fc7\u6c42\u89e3\u6cd5\u65b9\u7a0b\u5f97\u5230\u3002\u4e0a\u8ff0\u8fc7\u7a0b\u79f0\u4e3a\u591a\u5143\u51fd\u6570\u7684\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\u3002<\/p>\n<p>\u5728\u51fd\u6570\u8bba\u4e2d\uff0c\u9ad8\u7ef4\u7a7a\u95f4<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image064.png\" alt=\"img\" \/>\u4e2d\u7684\u57fa\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image065.png\" alt=\"img\" \/>\u7684\u6784\u9020\u4e5f\u6709\u8bb8\u591a\u65b9\u6cd5\u3002\u4e3a\u4e86\u7b80\u4fbf\uff0c\u5728\u8bb8\u591a\u65f6\u5019\u6211\u4eec\u91c7\u7528\u5f20\u91cf\u79ef\u5f62\u5f0f\u7684\u57fa\u51fd\u6570\uff0c\u5373\u6bcf\u4e2a\u57fa\u51fd\u6570\u662f\u5404\u4e2a\u7ef4\u6570\u7684\u4e00\u5143\u57fa\u51fd\u6570\u7684\u4e58\u79ef\u5f62\u5f0f\u3002\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u548c\u8ba1\u7b97\u673a\u8f85\u52a9\u51e0\u4f55\u8bbe\u8ba1\uff08CG&amp;CAGD\uff09\u9886\u57df\u7ecf\u5e38\u91c7\u7528\u3002<\/p>\n<p>4.2.      \u5411\u91cf\u503c\u51fd\u6570<\/p>\n<p>\u5982\u679c\u56e0\u53d8\u91cf\u6709\u591a\u4e2a\uff0c\u5373<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image059.png\" alt=\"img\" \/>\uff0c\u79f0\u4e3a\u5411\u91cf\u503c\u51fd\u6570\u3002\u6bd4\u5982\u7a7a\u95f4\u87ba\u65cb\u7ebf\u7684\u53c2\u6570\u65b9\u7a0b<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image069.png\" alt=\"img\" \/><\/th>\n<th>(4.3)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5c31\u662f\u4e00\u4e2a\u4ece\u4e00\u7ef4\u5230\u4e09\u7ef4\u7684\u5411\u91cf\u503c\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image070.png\" alt=\"img\" \/>\u3002\u5982\u679c\u81ea\u53d8\u91cf\u7684\u7ef4\u6570\u6bd4\u5e94\u53d8\u91cf\u7684\u7ef4\u6570\u4f4e\uff0c\u5219\u81ea\u53d8\u91cf\u53ef\u770b\u4f5c\u4e3a\u5e94\u53d8\u91cf\u7684\u53c2\u6570\u3002\u5728\u5f0f(4.3)\u4e2d\uff0c\u53d8\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image071.png\" alt=\"img\" \/>\u53ef\u770b\u4f5c\u4e3a\u8be5\u87ba\u65cb\u7ebf\u7684\u53c2\u6570\u3002<\/p>\n<p>\u5bf9\u4e8e\u5411\u91cf\u503c\u51fd\u6570\uff0c\u53ef\u4ee5\u770b\u6210\u662f\u591a\u4e2a\u4e00\u5143\u51fd\u6570\u6216\u591a\u5143\u51fd\u6570\uff08\u4e00\u822c\u5171\u4eab\u57fa\u51fd\u6570\uff09\u5373\u53ef\uff0c\u6240\u6709\u5904\u7406\u65b9\u6cd5\uff08\u5305\u62ec\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09\u90fd\u662f\u5bf9\u6bcf\u4e2a\u51fd\u6570\u5206\u522b\u64cd\u4f5c\u7684\uff0c\u4e0e\u524d\u9762\u5355\u4e2a\u51fd\u6570\u7684\u5904\u7406\u65b9\u6cd5\u5b8c\u5168\u4e00\u6837\u3002\u5982\u679c\u7528\u6570\u5b66\u65b9\u5f0f\u6765\u8868\u8fbe\uff0c\u524d\u9762\u7684\u5f88\u591a\u7b26\u53f7\u7531\u5411\u91cf\u53d8\u4e3a\u77e9\u9635\u7684\u5f62\u5f0f\u800c\u5df2\u3002\u8be6\u7ec6\u53ef\u67e5\u770b\u300a\u6570\u5b66\u5206\u6790\u300b\u3002<\/p>\n<h2><strong>\u4e94\u3001<\/strong>  <strong>\u53c2\u6570\u66f2\u7ebf\u66f2\u9762\u62df\u5408<\/strong><\/h2>\n<p>\u524d\u9762\u8ba8\u8bba\u7684\u51fd\u6570\u6240\u80fd\u8868\u8fbe\u7684\u66f2\u7ebf\u6bd4\u8f83\u7b80\u5355\uff0c\u65e0\u6cd5\u8868\u8fbe\u5c01\u95ed\u548c\u591a\u503c\u7684\u66f2\u7ebf\u3002\u56e0\u6b64\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u548c\u8ba1\u7b97\u673a\u8f85\u52a9\u51e0\u4f55\u8bbe\u8ba1\u4e2d\u5e38\u7528\u53c2\u6570\u66f2\u7ebf\u66f2\u9762\uff08\u672c\u8d28\u662f\u5411\u91cf\u503c\u51fd\u6570\uff0c\u89c14.2\u8282\uff09\u6765\u8868\u8fbe\u51e0\u4f55\u5f62\u72b6\uff0c\u7528\u4e8e\u51e0\u4f55\u9020\u578b\u3002\u53e6\u5916\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\u8fd8\u6709\u4e00\u79cd\u5229\u7528\u9690\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image072.png\" alt=\"img\" \/>\u6765\u8868\u8fbe\u66f2\u7ebf\u7684\u65b9\u5f0f\uff0c\u4e5f\u5e38\u7528\u4e8e\u9020\u578b\u4e2d\uff0c\u8fd9\u91cc\u4e0d\u5c55\u5f00\u4ecb\u7ecd\u3002<\/p>\n<p>5.1.      \u4e8c\u7ef4\u53c2\u6570\u66f2\u7ebf<\/p>\n<p>\u4ece\u6570\u5b66\u6765\u770b\uff0c\u4e00\u6761\u66f2\u7ebf\u7684\u672c\u5f81\u7ef4\u5ea6\u662f\u4e00\u7ef4\u7684\uff0c\u4e0d\u8bba\u662f\u4ece\u54ea\u4e2a\u7ef4\u5ea6\u7684\u7a7a\u95f4\u6765\u770b\u3002\u4ece\u76f4\u89c2\u6765\u770b\uff0c\u8be5\u66f2\u7ebf\u80fd\u88ab\u201c\u62c9\u201d\u6210\u4e3a\u4e00\u6761\u76f4\u7ebf\u6216\u7ebf\u6bb5\uff1b\u5373\uff0c\u4e00\u6761\u6709\u7aef\u70b9\u7684\u66f2\u7ebf\u80fd\u548c\u4e00\u6761\u7ebf\u6bb5\u5efa\u7acb1-1\u5bf9\u5e94\uff0c\u5982\u56fe5\uff08\u5de6\uff09\u6240\u793a\u3002\u56e0\u6b64\uff0c\u5d4c\u5165\u5230\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u66f2\u7ebf\u53ef\u7531\u5355\u4e2a\u53c2\u6570\u6765\u8868\u8fbe\uff0c\u5373\u6709\u5982\u4e0b\u5f62\u5f0f\u7684\u53c2\u6570\u5f62\u5f0f\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image073.png\" alt=\"img\" \/><\/th>\n<th>(5.1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image071.png\" alt=\"img\" \/>\u4e3a\u8be5\u66f2\u7ebf\u7684\u53c2\u6570\uff0c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image074.png\" alt=\"img\" \/>, <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image075.png\" alt=\"img\" \/>\u5747\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image071.png\" alt=\"img\" \/>\u7684\u51fd\u6570\uff0c\u5206\u522b\u8868\u793a\u66f2\u7ebf\u4e0a\u5bf9\u5e94\u4e8e\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image071.png\" alt=\"img\" \/>\u7684\u70b9\u7684\u4e24\u4e2a\u5750\u6807\u5206\u91cf\u3002\u4e00\u822c\u53c2\u6570\u66f2\u7ebf\u8868\u8fbe\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image076.png\" alt=\"img\" \/>\u3002\u672c\u8d28\u4e0a\uff0c\u8fd9\u662f\u4e00\u4e2a\u4ece<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image004.png\" alt=\"img\" \/>\u5230<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image077.png\" alt=\"img\" \/>\u7684\u5411\u91cf\u503c\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image078.png\" alt=\"img\" \/>\u3002<\/p>\n<p>5.2.      \u4e09\u7ef4\u53c2\u6570\u66f2\u9762<\/p>\n<p>\u7c7b\u4f3c\u5730\uff0c\u4e00\u5f20\u4e8c\u7ef4\u6d41\u5f62\u66f2\u9762\u7684\u672c\u5f81\u7ef4\u5ea6\u662f\u4e8c\u7ef4\u7684\u3002\u4e00\u5f20\u66f2\u9762\u80fd\u4e0e\u5e73\u9762\u4e0a\u7684\u4e00\u5757\u533a\u57df\u5efa\u7acb1-1\u5bf9\u5e94\uff0c\u5982\u56fe5\uff08\u53f3\uff09\u6240\u793a\u3002\u56e0\u6b64\uff0c\u5d4c\u5165\u5230\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u66f2\u9762\u53ef\u7531\u4e24\u4e2a\u53c2\u6570\u6765\u8868\u8fbe\uff0c\u5373\u6709\u5982\u4e0b\u5f62\u5f0f\u7684\u53c2\u6570\u5f62\u5f0f\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image079.png\" alt=\"img\" \/><\/th>\n<th>(5.2)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5176\u4e2d<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image080.png\" alt=\"img\" \/>\u4e3a\u8be5\u66f2\u9762\u7684\u53c2\u6570\uff0c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image081.png\" alt=\"img\" \/>, <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image082.png\" alt=\"img\" \/>\u5747\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image080.png\" alt=\"img\" \/>\u7684\u4e8c\u5143\u51fd\u6570\uff0c\u5206\u522b\u8868\u793a\u66f2\u9762\u4e0a\u5bf9\u5e94\u4e8e\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image080.png\" alt=\"img\" \/>\u7684\u70b9\u7684\u4e09\u4e2a\u5750\u6807\u5206\u91cf\u3002\u4e00\u822c\u53c2\u6570\u66f2\u9762\u8868\u8fbe\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image083.png\" alt=\"img\" \/>\u3002\u672c\u8d28\u4e0a\uff0c\u8fd9\u662f\u4e00\u4e2a\u4ece<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image077.png\" alt=\"img\" \/>\u5230<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image084.png\" alt=\"img\" \/>\u7684\u5411\u91cf\u503c\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image085.png\" alt=\"img\" \/>\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image086.jpg\" alt=\"img\" \/><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image087.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe5. \u53c2\u6570\u66f2\u7ebf\u66f2\u9762\u3002\u5de6\uff1a\u5355\u53c2\u6570\u66f2\u7ebf\uff1b\u53f3\uff1a\u53cc\u53c2\u6570\u66f2\u9762\u3002<\/p>\n<p>5.3.      \u53c2\u6570\u66f2\u7ebf\u66f2\u9762\u62df\u5408<\/p>\n<p>\u4e0b\u9762\u6211\u4eec\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528\u53c2\u6570\u66f2\u7ebf\u6765\u62df\u54082D\u5e73\u9762\u4e0a\u7684\u4e00\u7ec4\u6709\u5e8f\u6837\u672c\u70b9\u3002<\/p>\n<p>\u53c2\u6570\u66f2\u7ebf\u62df\u5408\u7684\u95ee\u9898\u63cf\u8ff0\u5982\u4e0b\uff1a\u7ed9\u5b9a\u5e73\u9762\u4e0a\u4e00\u7ec4\u6709\u5e8f\u6837\u672c\u70b9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image088.png\" alt=\"img\" \/>\uff0c\u6211\u4eec\u5e0c\u671b\u5bfb\u6c42\u4e00\u6761\u62df\u5408\u8fd9\u4e9b\u70b9\u7684\u53c2\u6570\u66f2\u7ebf\u5173\u7cfb<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image076.png\" alt=\"img\" \/>\u3002<\/p>\n<p>\u5982\u9700\u51b3\u5b9a\u4e00\u6761\u62df\u5408\u66f2\u7ebf\uff0c\u9996\u5148\u9700\u8981\u786e\u5b9a\u6bcf\u4e2a\u6837\u672c\u70b9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image089.png\" alt=\"img\" \/>\u6240\u5bf9\u5e94\u7684\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image090.png\" alt=\"img\" \/>\u3002\u5bf9\u4e8e\u4e00\u7ec4\u6709\u5e8f\u7684\u6837\u672c\u70b9\uff0c\u6240\u786e\u5b9a\u7684\u4e00\u79cd\u53c2\u6570\u5206\u5272\uff0c\u79f0\u4e4b\u4e3a\u8fd9\u7ec4\u6837\u672c\u70b9\u7684\u53c2\u6570\u5316\u3002\u53c2\u6570\u5316\u7684\u672c\u8d28\u5c31\u662f\u627e\u4e00\u7ec4\u6070\u5f53\u7684\u53c2\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image090.png\" alt=\"img\" \/>\u6765\u5339\u914d\u8fd9\u4e00\u7ec4\u6837\u672c\u70b9\uff0c\u4ee5\u4fbf\u4f7f\u8fd9\u6761\u62df\u5408\u51fa\u6765\u7684\u66f2\u7ebf\u7f8e\u89c2\u3001\u5408\u7406\u3002<\/p>\n<p>\u5728\u53c2\u6570\u66f2\u7ebf\u62df\u5408\u4e2d\uff0c\u6837\u672c\u70b9\u7684\u53c2\u6570\u5316\u662f\u4e2a\u975e\u5e38\u57fa\u672c\u800c\u91cd\u8981\u7684\u95ee\u9898\u3002\u4e0d\u540c\u7684\u53c2\u6570\u5316\uff0c\u5bf9\u62df\u5408\u66f2\u7ebf\u7684\u5f62\u72b6\u4f1a\u4ea7\u751f\u5f88\u5927\u7684\u5f71\u54cd\u3002\u56fe6\u663e\u793a\u4e86\u4e09\u79cd\u53c2\u6570\u5316\uff08\u5747\u5300\u53c2\u6570\u5316\u3001\u5f26\u957f\u53c2\u6570\u5316\u548c\u4e2d\u5fc3\u53c2\u6570\u5316\uff09\u5bf9\u62df\u5408\u66f2\u7ebf\u5f62\u72b6\u7684\u5f71\u54cd\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image091.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe6. \u4e0d\u540c\u7684\u53c2\u6570\u5316\u5bfc\u81f4\u4e0d\u540c\u7684\u53c2\u6570\u66f2\u7ebf\u62df\u5408\u7ed3\u679c\u3002<\/p>\n<p>\u7c7b\u4f3c\u5730\uff0c\u5982\u679c\u5229\u7528\u53c2\u6570\u66f2\u9762\u6765\u62df\u5408<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image084.png\" alt=\"img\" \/>\u7a7a\u95f4\u4e2d\u7ed9\u5b9a\u7684\u4e00\u7ec4\u6837\u672c\u70b9\uff0c\u9996\u5148\u4e5f\u9700\u8981\u786e\u5b9a\u8fd9\u4e9b\u6837\u672c\u70b9\u5728<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image077.png\" alt=\"img\" \/>\u5e73\u9762\u4e0a\u7684\u53c2\u6570\u5316\uff0c\u5982\u56fe7\u6240\u793a\u3002\u5728\u66f2\u9762\u53c2\u6570\u5316\u4e2d\uff0c\u4e0d\u4ec5\u9700\u8981\u5efa\u7acb\u6837\u672c\u70b9\u53ca\u5176\u53c2\u6570\u7684\u4e00\u4e00\u5bf9\u5e94\uff0c\u6211\u4eec\u8fd8\u5e0c\u671b\u53c2\u6570\u533a\u57df\u7684\u7f51\u683c\u4fdd\u6301\u539f\u59cb\u7f51\u683c\u7684\u4e00\u4e9b\u91cd\u8981\u7684\u51e0\u4f55\u7279\u6027\uff0c\u6bd4\u5982\u89d2\u5ea6\u3001\u8fb9\u957f\u7b49\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image092.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe7. \u4e09\u7ef4\u66f2\u9762\u7684\u53c2\u6570\u5316\u3002<\/p>\n<p>\u66f2\u9762\u53c2\u6570\u5316\u662f\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\u975e\u5e38\u57fa\u7840\u4e14\u91cd\u8981\u7684\u4e00\u4e2a\u7814\u7a76\u8bfe\u9898\uff0c\u4e5f\u4e00\u76f4\u662f\u7814\u7a76\u70ed\u70b9\u4e4b\u4e00\u3002\u7b14\u8005\u53ca\u6240\u5728\u7684\u8bfe\u9898\u7ec4\u4e5f\u5728\u8fd9\u4e2a\u8bfe\u9898\u65b9\u9762\u4f5c\u4e86\u5927\u91cf\u7684\u5de5\u4f5c\uff0c\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u8be6\u7ec6\u67e5\u770b<a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/\">\u7b14\u8005\u7684\u76f8\u5173\u8bba\u6587<\/a>\uff1a<\/p>\n<p>\uff08\u5e73\u9762\u53c2\u6570\u5316\uff09<\/p>\n<p>[5-1] Ligang Liu, Lei Zhang, Yin Xu, Craig Gotsman, Steven J. Gortler. A Local\/Global Approach to Mesh Parameterization. Computer Graphics Forum (Proc. Eurographics Symposium on Geometry Processing (SGP)), 27(5), 1495-1504, 2008.<\/p>\n<p>[5-2] Ligang Liu, Chunyang Ye, Ruiqi Ni, Xiao-Ming Fu. Progressive Parameterizations. ACM Transactions on Graphics (Proc. Siggraph), 37(4), Article 41: 1-12, 2018.<\/p>\n<p>\uff08\u7403\u9762\u53c2\u6570\u5316\uff09<\/p>\n<p>[5-3] Xin Hu, Xiao-Ming Fu, Ligang Liu. Advanced Hierarchical Spherical Parameterizations. IEEE Transactions on Visualization and Computer Graphics, to appear, 2018.<\/p>\n<p>[5-4] Chunxue Wang, Xin Hu, Xiaoming Fu, Ligang Liu. Bijective Spherical Parametrization with Low Distortion. Computers&amp;Graphics (Proc. SMI), 58: 161-171, 2016.<\/p>\n<p>[5-5] Chunxue Wang, Zheng Liu, Ligang Liu. As-Rigid-As-Possible Spherical Parameterization. Graphical Models (Proc. GMP), 76(5): 457-467, 2014.<\/p>\n<p>\uff08\u6d41\u5f62\u53c2\u6570\u5316\uff09<\/p>\n<p>[5-6] Lei Zhang, Ligang Liu, Zhongping Ji, Guojin Wang. Manifold Parameterization. Lecture Notes in Computer Science (Proc. Computer Graphics International), 4035, 160-171, 2006.<\/p>\n<h2><strong>\u516d\u3001<\/strong>  <strong>\u4ece\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u89c2\u70b9\u6765\u770b\u62df\u5408\u51fd\u6570<\/strong><\/h2>\n<p>\u4e3a\u4e86\u8bb2\u6e05\u695a\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff08Artificial Neural Network\uff0cANN\uff09\uff0c\u4e0b\u9762\u6211\u4eec\u5148\u4ece\u795e\u7ecf\u7f51\u7edc\u7684\u89c2\u70b9\u6765\u770b\u4f20\u7edf\u7684\u62df\u5408\u51fd\u6570\u548c\u66f2\u7ebf\u66f2\u9762\u3002<\/p>\n<p>6.1.      \u4e00\u5143\u51fd\u6570<\/p>\n<p>\u5bf9\u4e8e\u4e00\u5143\u7684\u903c\u8fd1\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image006.png\" alt=\"img\" \/><\/p>\n<table>\n<thead>\n<tr>\n<th><\/th>\n<th><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image037.png\" alt=\"img\" \/>.<\/th>\n<th>(6.1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u53ef\u4ee5\u770b\u6210\u4e3a\u5982\u56fe8\u7684\u4e09\u5c42\u795e\u7ecf\u7f51\u7edc\uff0c\u5176\u4e2d\u53ea\u6709\u4e00\u4e2a\u9690\u5c42\u3002\u9690\u5c42\u4e0a\u6709<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u4e2a\u8282\u70b9\uff0c\u6fc0\u6d3b\u51fd\u6570\u5206\u522b\u4e3a\u57fa\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image093.png\" alt=\"img\" \/>\uff08\u4ece\u8fd9\u91cc\u6211\u4eec\u5c06\u57fa\u51fd\u6570\u79f0\u4e3a\u201c\u6fc0\u6d3b\u51fd\u6570\u201d\uff09\u3002\u8f93\u5165\u5c42\u5230\u9690\u5c42\u7684\u6743\u8bbe\u4e3a\u5e38\u503c1\uff08\u56fe8\u5de6\uff09\uff0c\u4e5f\u53ef\u4ee5\u770b\u6210\u4e3a\u5c06\u8f93\u5165\u5c42\u7684\u503c\u201c\u76f4\u63a5\u4ee3\u5165\u201d\uff08\u4e0d\u505a\u4efb\u4f55\u53d8\u6362\uff0c\u7528\u865a\u7ebf\u8868\u793a\uff09\u5230\u6fc0\u6d3b\u51fd\u6570\uff08\u56fe8\u53f3\uff09\u3002\u9690\u5c42\u5230\u8f93\u51fa\u5c42\u7684\u6743\u4e3a\u57fa\u51fd\u6570\u7684\u7ec4\u5408\u7cfb\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image094.png\" alt=\"img\" \/>\u3002<\/p>\n<p>\u4e2d\u95f4\u9690\u5c42\u7684\u8f93\u51fa\u8282\u70b9\u6240\u5f62\u6210\u7684\u5411\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image095.png\" alt=\"img\" \/>\u53ef\u770b\u4f5c\u4e3a\u8f93\u5165\u91cf\u7684\u201c\u7279\u5f81\u201d\u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5f00\u59cb\u7528\u673a\u5668\u5b66\u4e60\u7684\u8bed\u8a00\u6765\u63cf\u8ff0\u6570\u636e\u62df\u5408\u7684\u8fc7\u7a0b\u3002\u6574\u4e2a\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u7531\u4e2d\u95f4\u8282\u70b9\u7684\u6fc0\u6d3b\u51fd\u6570\u53ca\u6743\u7cfb\u6570\u6240\u51b3\u5b9a\u7684\u4e00\u4e2a\u51fd\u6570(6.1)\u3002\u6211\u4eec\u79f0\u6837\u672c\u70b9<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image008.png\" alt=\"img\" \/>, \u4e3a\u8bad\u7ec3\u6570\u636e\uff08Training set\uff09\uff0c\u79f0\u51fd\u6570\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u7684\u8bef\u5dee\u5ea6\u91cf\u4e3a\u635f\u5931\u51fd\u6570\uff08Loss function\uff09\u3002\u901a\u8fc7\u8bad\u7ec3\u6570\u636e\u6765\u6781\u5c0f\u5316\u635f\u5931\u51fd\u6570\u5f97\u5230\u6743\u7cfb\u6570\u7684\u8fc7\u7a0b\u79f0\u4e3a\u201c\u8bad\u7ec3\u201d\u6216\u201c\u5b66\u4e60\u201d\u3002\u5982\u679c\u635f\u5931\u51fd\u6570\u53d6\u4e3a(1.3)\u7684\u5f62\u5f0f\uff0c\u5219\u7f51\u7edc\u7684\u8bad\u7ec3\u8fc7\u7a0b\u672c\u8d28\u4e0a\u5c31\u662f\u524d\u9762\u6240\u8bb2\u7684\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff082.4\u8282\uff09\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image096.jpg\" alt=\"img\" \/>   <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image097.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe8. 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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u53ef\u770b\u6210\u4e3a\u5982\u4e0b\u56fe\u7684\u4e00\u4e2a\u4e09\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\u3002\u6ce8\u610f\u8fd9\u91cc\u9690\u5c42\u7684\u6fc0\u6d3b\u51fd\u6570\u90fd\u662f<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image007.png\" alt=\"img\" \/>\u7ef4\u51fd\u6570\uff0c\u4ece\u8f93\u5165\u5c42\u5230\u9690\u5c42\u4e5f\u662f\u76f4\u63a5\u4ee3\u5165\u3002\u8f93\u51fa\u5c42\u7684\u5404\u4e2a\u5206\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image099.png\" alt=\"img\" \/>\u5171\u4eab\u9690\u5c42\u7684\u6fc0\u6d3b\u51fd\u6570\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image100.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe9. 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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image101.png\" alt=\"img\" \/>\uff1b\u9690\u5c423\u7684\u6fc0\u6d3b\u51fd\u6570\u4e3a\u5355\u53d8\u91cf\u57fa\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image102.png\" alt=\"img\" \/>\u3002\u4e2d\u95f4\u9690\u5c42\uff08\u9690\u5c421\u30012\u30013\uff09\u7684\u8f93\u51fa\u8282\u70b9\u6240\u5f62\u6210\u7684\u5411\u91cf\u5747\u53ef\u5206\u522b\u770b\u4f5c\u4e3a\u8f93\u5165\u91cf\u5728\u4e0d\u540c\u7ef4\u6570\u7a7a\u95f4\u7684\u201c\u7279\u5f81\u201d\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image103.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe10. \u62df\u5408\u66f2\u7ebf\u7684\u795e\u7ecf\u7f51\u7edc\u3002\u8f93\u5165\u5c42\uff08\u6837\u672c\u70b9\uff09\u5230\u53c2\u6570\u5316\u662f\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u53d8\u6362\uff1b<\/p>\n<p>\u53c2\u6570\u5316\u5230\u8f93\u51fa\u5c42\u662f\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u53d8\u6362\u3002<\/p>\n<p>\u7c7b\u4f3c\u5730\uff0c\u62df\u5408\u66f2\u9762\u4e5f\u53ef\u4ee5\u770b\u4f5c\u4e3a\u4e00\u4e2a\u5982\u4e0b\u56fe\u7684\u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image104.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe11. \u62df\u5408\u66f2\u9762\u7684\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n<p>\u4ece\u66f2\u7ebf\u66f2\u9762\u62df\u5408\u7684\u8fc7\u7a0b\u53ca\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u6765\u770b\uff0c\u5982\u679c\u5c06\u6574\u4e2a\u7f51\u7edc\u8fdb\u884c\u4f18\u5316\uff0c\u5219\u62df\u5408\u7684\u8fc7\u7a0b\u662f\u5bfb\u6c42\u6837\u672c\u70b9\u7684\u53c2\u6570\u5316\u4ee5\u53ca\u8868\u8fbe\u51fd\u6570\u7684\u57fa\u51fd\u6570\uff0c\u4f7f\u5f97\u62df\u5408\u8bef\u5dee\u6781\u5c0f\u5316\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u662f\u77e5\u9053\u7ed9\u5b9a\u6837\u672c\u70b9\u7684\u201c\u672c\u5f81\u7ef4\u6570\u201d\uff0c\u56e0\u6b64\uff0c\u4eba\u4e3a\u8bbe\u7f6e\u4e86\u7b2c\u4e00\u4e2a\u9690\u5c42\u7684\u7ef4\u6570\u4e3a1\uff08\u66f2\u7ebf\uff09\u62162\uff08\u66f2\u9762\uff09\u3002\u7136\u800c\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u6570\u636e\u7684\u672c\u5f81\u7ef4\u6570\uff0c\u6b64\u65f6\u9700\u8981\u5229\u7528\u5176\u4ed6\u65b9\u6cd5\uff08\u6bd4\u5982\u6d41\u5f62\u5b66\u4e60\u6216\u964d\u7ef4\u65b9\u6cd5\uff09\u6765\u201c\u68c0\u6d4b\u201d\u6216\u201c\u731c\u6d4b\u201d\u9690\u5c42\u7684\u7ef4\u6570\uff0c\u6216\u8005\u76f4\u63a5\u6839\u636e\u7ecf\u9a8c\u6765\u4e0d\u65ad\u8c03\u53c2\u548c\u6d4b\u8bd5\u3002<\/p>\n<p>\u9700\u8981\u63d0\u53ca\u7684\u662f\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0c\u4f20\u7edf\u7684\u5927\u90e8\u5206\u65b9\u6cd5\u662f\u5c06\u53c2\u6570\u5316\u7684\u95ee\u9898\u548c\u66f2\u7ebf\u66f2\u9762\u62df\u5408\u95ee\u9898\u5206\u4e3a\u4e24\u4e2a\u95ee\u9898\u6765\u89e3\u51b3\u3002\u6709\u4e9b\u5de5\u4f5c\u4e13\u95e8\u505a\u53c2\u6570\u5316\uff0c\u6709\u4e9b\u5de5\u4f5c\u4e13\u95e8\u7814\u7a76\u62df\u5408\u95ee\u9898\u3002\u5176\u4e2d\u53c2\u6570\u5316\u7684\u5de5\u4f5c\u66f4\u4e3a\u91cd\u8981\uff0c\u76f4\u63a5\u51b3\u5b9a\u4e86\u62df\u5408\u66f2\u7ebf\u66f2\u9762\u7684\u8d28\u91cf\u3002\u6b64\u5904\u4e0d\u8be6\u8ff0\u3002<\/p>\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u672c\u8282\u53ea\u662f\u4ece\u795e\u7ecf\u7f51\u7edc\u7684\u89c2\u70b9\u6765\u770b\u66f2\u7ebf\u66f2\u9762\u7684\u53c2\u6570\u5316\u548c\u62df\u5408\u7684\u95ee\u9898\u3002\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0c\u6211\u4eec\u4e0d\u662f\u7b80\u5355\u7684\u901a\u8fc7\u4e0a\u8ff0\u7f51\u7edc\u6765\u6c42\u53c2\u6570\u5316\uff08\u5355\u4e2a\u6837\u672c\u70b9\uff09\uff0c\u800c\u662f\u8981\u8003\u8651\u66f4\u591a\u7684\u6837\u672c\u70b9\u4e00\u8d77\u6765\u6c42\u89e3\u53c2\u6570\u5316\u3002\u8fd9\u4e2a\u540e\u9762\u8fd8\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u3002<\/p>\n<h2><strong>\u4e03\u3001<\/strong>  <strong>\u901a\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc<\/strong><\/h2>\n<p>\u6709\u4e86\u4e0a\u8ff0\u7684\u7406\u89e3\uff0c\u6211\u4eec\u73b0\u5728\u6765\u7406\u89e3\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u5c31\u975e\u5e38\u5bb9\u6613\u4e86\u3002<\/p>\n<p>7.1.      \u51fd\u6570\u62df\u5408\u56de\u987e<\/p>\n<p>\u56de\u987e\u524d\u9762\u6240\u8ff0\u7684\u51fd\u6570\u903c\u8fd1\u8bba\u4e2d\u7684\u51fd\u6570\u62df\u5408\u95ee\u9898\uff0c\u59cb\u7ec8\u662f\u5b58\u5728\u7740\u4e24\u4e2a\u201c\u7ea0\u7ed3\u201d\u3002\u4e00\u662f\u9009\u62e9\u4ec0\u4e48\u6837\u7684\u903c\u8fd1\u51fd\u6570\u7c7b\uff0c\u5373\u9009\u62e9\u4ec0\u4e48\u7c7b\u578b\u7684\u57fa\u51fd\u6570\uff1f\u4e8c\u662f\u9009\u62e9\u591a\u9ad8\u7684\u6b21\u6570\u6216\u9636\u6570\uff1f<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4ece\u56fe8\u6216\u56fe9\u7684\u795e\u7ecf\u7f51\u7edc\u7684\u89c2\u70b9\u6765\u770b\uff0c\u7f51\u7edc\u7684\u7ed3\u6784\u8bbe\u7f6e\u90fd\u5b58\u5728\u7740\u5982\u4e0b\u4e24\u4e2a\u201c\u7ea0\u7ed3\u201d\uff1a<\/p>\n<p>\\1.   \u9690\u5c42\u4e2d\u7684\u8282\u70b9\u4e2d\u4f7f\u7528\u4ec0\u4e48\u6837\u7684\u6fc0\u6d3b\u51fd\u6570\uff08\u57fa\u51fd\u6570\uff09\uff1f<\/p>\n<p>\\2.   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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image106.png\" alt=\"img\" \/>\u65b9\u5411\u7684\u4f38\u7f29\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image108.png\" alt=\"img\" \/>\u90fd\u4e0e\u539f\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image109.png\" alt=\"img\" \/>\u7ebf\u6027\u65e0\u5173\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u80fd\u6709\u8db3\u591f\u591a\u7684\u53d8\u6362\u6240\u751f\u6210\u7684\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image110.png\" alt=\"img\" \/>\uff0c\u5176\u7ebf\u6027\u7ec4\u5408\u6240\u5f20\u6210\u7684\u51fd\u6570\u7a7a\u95f4\u5c31\u80fd\u6709\u5145\u5206\u7684\u8868\u8fbe\u80fd\u529b\u3002\u90a3\u4e48\u8fd9\u4e9b\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image111.png\" alt=\"img\" \/>\uff08\u53ef\u80fd\u90fd\u7ebf\u6027\u65e0\u5173\uff09\u662f\u5426\u80fd\u6784\u6210\u903c\u8fd1\u4e00\u822c\u51fd\u6570\u7684\u201c\u57fa\u51fd\u6570\u201d\u5462\uff1f<\/p>\n<p>\u4e00\u4e2a\u81ea\u7136\u7684\u60f3\u6cd5\u5c31\u662f\uff0c\u6211\u4eec\u80fd\u5426\u4ee5\u8fd9\u4e2a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image105.png\" alt=\"img\" \/>\u4f5c\u4e3a\u6fc0\u6d3b\u51fd\u6570\uff0c\u8ba9\u7f51\u7edc\u81ea\u52a8\u5730\u53bb\u5b66\u4e60\u8fd9\u4e9b\u6fc0\u6d3b\u51fd\u6570\u7684\u53d8\u6362<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image112.png\" alt=\"img\" \/>\uff0c\u6216\u8005\u8bf4\u53bb\u5b66\u4e60\u4e00\u4e9b\u201c\u57fa\u51fd\u6570\u201d\uff0c\u6765\u8868\u8fbe\u6240\u9700\u8981\u7684\u62df\u5408\u51fd\u6570\u5462\uff1f\u8fd9\u5c31\u662f\u56fe12\u6240\u793a\u7684\u795e\u7ecf\u5143\u3002\u53d8\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image106.png\" alt=\"img\" \/>\u4e58\u4ee5\u4e00\u4e2a\u4f38\u7f29\uff0c\u52a0\u4e0a\u4e00\u4e2a\u5e73\u79fb\uff08\u79f0\u4e3a\u504f\u7f6e\u201cbias\u201d\uff09\uff0c\u5373\u53d8\u91cf\u7684\u4eff\u5c04\u53d8\u6362\uff0c\u6210\u4e3a\u795e\u7ecf\u5143\u7684\u8f93\u5165<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image113.png\" alt=\"img\" \/>\uff1b\u7136\u540e\u901a\u8fc7\u6fc0\u6d3b\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image114.png\" alt=\"img\" \/>\u590d\u5408\u540e\u6210\u4e3a\u8be5\u795e\u7ecf\u5143\u7684\u8f93\u51fa<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image115.png\" alt=\"img\" \/>\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image116.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe12. 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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image115.png\" alt=\"img\" \/>\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image119.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe13. \u591a\u5143\uff08\u591a\u53d8\u91cf\uff09\u51fd\u6570\u7684\u795e\u7ecf\u5143\u7ed3\u6784\u3002<\/p>\n<p>\u4e0d\u5931\u4e00\u822c\u6027\uff0c\u6211\u4eec\u4e0b\u9762\u5c31\u76f4\u63a5\u4ee5\u591a\u5143\u51fd\u6570\u7684\u5f62\u5f0f\u6765\u4ecb\u7ecd\u4e00\u822c\u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u6784\u3002\u5bf9\u4e8e\u5411\u91cf\u503c\u51fd\u6570\uff08<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image120.png\" alt=\"img\" \/>\u662f\u591a\u7ef4\u7684\uff09\uff0c\u5219\u5206\u522b\u5c06<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image120.png\" alt=\"img\" \/>\u7684\u5404\u4e2a\u7ef4\u6570\u5206\u522b\u770b\u4f5c\u4e00\u4e2a\u591a\u5143\u51fd\u6570\u5904\u7406\u800c\u5df2\uff0c\u8fd9\u4e9b\u51fd\u6570\u5171\u4eab\u8282\u70b9\uff08\u57fa\u51fd\u6570\uff09\u5373\u53ef\u3002<\/p>\n<p>7.3.      \u5355\u9690\u5c42\u795e\u7ecf\u7f51\u7edc<\/p>\n<p>\u4e00\u4e2a\u591a\u5143\u51fd\u6570\u7684\u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u6784\u5982\u56fe14\u6240\u793a\uff0c\u6709\u4e00\u4e2a\u8f93\u5165\u5c42\uff0c\u4e00\u4e2a\u9690\u5c42\u53ca\u4e00\u4e2a\u8f93\u51fa\u5c42\u3002\u8f93\u5165\u5c42\u9664\u4e86\u53d8\u91cf<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image117.png\" alt=\"img\" \/>\u5916\uff0c\u8fd8\u6709\u4e00\u4e2a\u5e38\u6570\u8282\u70b91\uff1b\u9690\u5c42\u5305\u542b\u591a\u4e2a\u8282\u70b9\uff0c\u6bcf\u4e2a\u8282\u70b9\u7684\u6fc0\u6d3b\u51fd\u6570\u90fd\u662f<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image114.png\" alt=\"img\" 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\/>\uff0c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image125.png\" alt=\"img\" \/>\uff08\u8f93\u5165\u5c42\u4e0e\u9690\u5c42\u4e4b\u95f4\u7684\u6743\u53ca\u504f\u7f6e\u9879\uff09\u53ca<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image126.png\" alt=\"img\" \/>\uff08\u9690\u5c42\u4e0e\u8f93\u51fa\u5c42\u4e4b\u95f4\u7684\u6743\uff0c\u6b64\u5c42\u4e00\u822c\u4e0d\u7528\u504f\u7f6e\u9879\uff09\u4f5c\u4e3a\u8fd9\u4e2a\u795e\u7ecf\u7f51\u7edc\u7684\u53c2\u6570\u53d8\u91cf\uff0c\u9700\u8981\u901a\u8fc7\u6781\u5c0f\u5316\u635f\u5931\u51fd\u6570\u6765\u6c42\u89e3\u7684\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u79f0\u4e3a\u201c\u8bad\u7ec3\u201d\u6216\u201c\u5b66\u4e60\u201d\u3002<\/p>\n<p>\u4e0e\u524d\u9762\u6240\u8ff0\u7684\u903c\u8fd1\u8bba\u4e2d\u7684\u62df\u5408\u51fd\u6570\u7c7b\u4f3c\uff0c\u7f51\u7edc\u7684\u9690\u5c42\u7684\u8282\u70b9\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u662f\u9700\u8981\u901a\u8fc7\u4e0d\u65ad\u8c03\u8bd5\u548c\u5c1d\u8bd5\u6765\u786e\u5b9a\u7684\u3002\u9690\u5c42\u7684\u8282\u70b9\u8f93\u51fa<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image127.png\" alt=\"img\" \/>\u79f0\u4e3a\u8f93\u5165\u6570\u636e<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image128.png\" alt=\"img\" \/>)\u7684\u201c\u7279\u5f81\u201d\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image129.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe14. 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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image105.png\" alt=\"img\" \/>\u7ecf\u8fc7\u5145\u5206\u591a\u7684\u5e73\u79fb\u548c\u4f38\u7f29\uff08\u5305\u62ec\u5b83\u4eec\u7684\u7ec4\u5408<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image132.png\" alt=\"img\" \/>\uff09\u6240\u7ebf\u6027\u5f20\u6210\u7684\u51fd\u6570\u7a7a\u95f4\uff0c\u5176\u8868\u8fbe\u80fd\u529b\u6709\u591a\u5f3a\uff1f\u8fd9\u4e2a\u51fd\u6570\u7a7a\u95f4\u662f\u5426\u5728\u6240\u6709\u51fd\u6570\u7a7a\u95f4\u662f\u7a20\u5bc6\u7684\uff1f\u5982\u679c\u95ee\u9898\u662f\u6b63\u786e\u7684\uff0c\u90a3\u4e48\u5c31\u662f\u8bf4\uff0c\u5bf9\u4e8e\u4efb\u4f55\u4e00\u4e2a\u7ed9\u5b9a\u7684\u51fd\u6570\uff0c\u603b\u80fd\u627e\u5230\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image105.png\" alt=\"img\" \/>\u7684\u591a\u6b21\u5e73\u79fb\u548c\u7f29\u653e\u7684\u51fd\u6570\uff0c\u5176\u7ebf\u6027\u7ec4\u5408\u80fd\u591f\u903c\u8fd1\u7ed9\u5b9a\u7684\u8fd9\u4e2a\u51fd\u6570\uff1b\u4e5f\u5c31\u662f\u8bf4\uff0c\u56fe14\u4e2d\u7684\u795e\u7ecf\u7f51\u7edc\u53ea\u8981\u9690\u5c42\u7684\u8282\u70b9\u6570\u8db3\u591f\u591a\uff0c\u8be5\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\u5c31\u80fd\u903c\u8fd1\u4efb\u610f\u7684\u51fd\u6570\u3002<\/p>\n<p>\u5e78\u8fd0\u7684\u662f\uff0c\u4e0a\u8ff0\u731c\u60f3\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\u662f\u6210\u7acb\u7684\uff01\u6709\u4ee5\u4e0b\u7684\u4e07\u80fd\u903c\u8fd1\u5b9a\u7406\u6240\u4fdd\u8bc1\u3002<\/p>\n<p>7.4.      \u4e07\u80fd\u903c\u8fd1\u5b9a\u7406<\/p>\n<p>\u8bb0<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image133.png\" alt=\"img\" \/>\u4e3a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image064.png\" alt=\"img\" 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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image135.png\" alt=\"img\" \/>\u4e0a\u76f8\u5bf9\u6d4b\u5ea6<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image138.png\" alt=\"img\" \/>\u7684\u53ef\u79ef\u51fd\u6570\u7a7a\u95f4\uff08\u5373<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image139.png\" alt=\"img\" \/>\uff09\u3002<\/p>\n<p>\u8bbe\u7ed9\u5b9a\u4e00\u5143\u6fc0\u6d3b\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image140.png\" alt=\"img\" \/>\uff0c\u9996\u5148\u7ed9\u51fa\u5982\u4e0b\u5b9a\u4e49\u3002<\/p>\n<p>\u3010\u5b9a\u4e497.1\u3011\u79f0\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image141.png\" alt=\"img\" \/>\u4e3a\u538b\u7f29\u51fd\u6570\uff0c\u5982\u679c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image141.png\" alt=\"img\" \/>\u5355\u8c03\u4e0d\u51cf\uff0c\u4e14\u6ee1\u8db3<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image142.png\" alt=\"img\" \/>, <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image143.png\" alt=\"img\" \/> .<\/p>\n<p>\u3010\u5b9a\u4e497.2\u3011\u79f0\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image141.png\" alt=\"img\" \/>\u4e3a\u53ef\u5206\u8fa8\u7684\uff0c\u82e5\u5bf9\u4e8e\u6709\u9650\u6d4b\u5ea6<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image138.png\" alt=\"img\" \/>\uff0c\u7531<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image144.png\" alt=\"img\" \/>,<\/p>\n<p>\u53ef\u5f97\u5230<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image145.png\" alt=\"img\" \/><\/p>\n<p>\u3010\u5b9a\u4e497.3\u3011\u8bb0<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image146.png\" alt=\"img\" \/><\/p>\n<p>\u4e3a\u6240\u6709\u7531\u6fc0\u6d3b\u51fd\u6570\u53d8\u6362\u53ca\u7ebf\u6027\u7d2f\u52a0\u6240\u6784\u6210\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image007.png\" alt=\"img\" \/>\u7ef4\u51fd\u6570\u7a7a\u95f4\uff08\u5373\u5177\u6709<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u4e2a\u8282\u70b9\u7684\u5355\u9690\u5c42\u795e\u7ecf\u7f51\u7edc\u6240\u8868\u8fbe\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image007.png\" alt=\"img\" \/>\u7ef4\u51fd\u6570\uff09\u3002<\/p>\n<p>\u3010\u5b9a\u74067.1\u3011\u82e5<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image147.png\" alt=\"img\" \/>\u662f\u538b\u7f29\u51fd\u6570\uff0c\u5219<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image148.png\" alt=\"img\" \/>\u5728<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image134.png\" alt=\"img\" \/>\u4e2d\u4e00\u81f4\u7a20\u5bc6\uff0c\u5728<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image136.png\" alt=\"img\" \/>\u4e2d\u6309\u5982\u4e0b\u8ddd\u79bb<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image149.png\" alt=\"img\" \/>\u4e0b\u7a20\u5bc6\uff1a<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image150.png\" alt=\"img\" \/>.<\/p>\n<p>\u3010\u5b9a\u74067.2\u3011\u82e5<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image147.png\" alt=\"img\" \/>\u662f\u53ef\u5206\u8fa8\u7684\uff0c\u5219<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image148.png\" alt=\"img\" \/>\u5728<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image134.png\" alt=\"img\" \/>\u4e2d\u6309\u8fde\u7eed\u51fd\u6570\u8ddd\u79bb\u4e0b\u7a20\u5bc6\u3002<\/p>\n<p>\u3010\u5b9a\u74067.3\u3011\u82e5<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image147.png\" alt=\"img\" \/>\u662f\u8fde\u7eed\u6709\u754c\u7684\u975e\u5e38\u503c\u51fd\u6570\uff0c\u5219<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image148.png\" alt=\"img\" \/>\u5728<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image134.png\" alt=\"img\" 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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image021.png\" alt=\"img\" \/>\uff0c\u53ea\u8981\u9879\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image022.png\" alt=\"img\" \/>\u8db3\u591f\u591a\uff0c<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image148.png\" alt=\"img\" \/>\u4e2d\u5c31\u5b58\u5728\u4e00\u4e2a\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\uff0c\u4f7f\u5f97<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image020.png\" alt=\"img\" \/>\u5728\u4e00\u5b9a\u7cbe\u5ea6\u4e0b\u903c\u8fd1<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image021.png\" alt=\"img\" \/>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u56fe14\u6240\u8868\u8fbe\u7684\u5355\u9690\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\u6240\u8868\u8fbe\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image007.png\" alt=\"img\" \/>\u7ef4\u51fd\u6570\u80fd\u591f\u903c\u8fd1<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image064.png\" alt=\"img\" \/>\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u51fd\u6570\u3002<\/p>\n<p>\u6839\u636e\u4e0a\u8ff0\u5b9a\u7406\u53ef\u77e5\uff0c\u51fd\u6570<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image147.png\" alt=\"img\" \/>\u53ea\u8981\u6ee1\u8db3\u4e00\u5b9a\u6761\u4ef6\u5373\u53ef\u4f5c\u4e3a\u4e00\u4e2a\u5408\u9002\u7684\u6fc0\u6d3b\u51fd\u6570\u3002\u4f46\u8fd8\u662f\u5b58\u5728\u7740\u4e00\u4e2a\u5de8\u5927\u7684\u201c\u7ea0\u7ed3\u201d\uff0c\u5c31\u662f\u9690\u5c42\u4e2d\u7684\u8282\u70b9\u6570\u91cf\u8be5\u53d6\u591a\u5927\uff0c\u4ecd\u662f\u672a\u77e5\u7684\u3002\u5728\u5b9e\u9645\u4e2d\uff0c\u8fd9\u4e2a\u662f\u8981\u4e0d\u65ad\u901a\u8fc7\u6d4b\u8bd5\u548c\u8c03\u8bd5\u6765\u51b3\u5b9a\u7684\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u79f0\u4e3a\u201c\u8c03\u53c2\u201d\u3002<\/p>\n<p>\u5b9a\u74067.1-7.4\u7684\u8be6\u7ec6\u8bc1\u660e\u53ef\u89c1\u4ee5\u4e0b\u8bba\u6587\u3002<\/p>\n<p>[7-1] K. Hornik, et al. Multilayer feedforward networks are universal approximations. Neural Networks, 2: 359-366, 1989.<\/p>\n<p>[7-2] G. Cybenko. Approximation by superpositions of a sigmoidal function. Math. Control Signals System, 2: 303-314, 1989.<\/p>\n<p>[7-3] K. Hornik. Approximation capabilities of multilayer feedforward networks. Neural Networks, 4: 251-257, 1991.<\/p>\n<p>7.5.      \u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff1a\u591a\u9690\u5c42\u795e\u7ecf\u7f51\u7edc<\/p>\n<p>\u5c06\u4e0a\u8ff0\u7684\u795e\u7ecf\u7f51\u7edc\u7684\u9690\u5c42\u8fdb\u4e00\u6b65\u63a8\u5e7f\u5230\u591a\u5c42\uff0c\u5373\u53ef\u5f97\u5230\u591a\u9690\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u5373\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff08\u6df1\u5ea6\u7684\u610f\u601d\u5c31\u662f\u591a\u5c42\uff09\u3002\u5176\u7f51\u7edc\u7ed3\u6784\u5982\u56fe15\u6240\u793a\u3002<\/p>\n<p>\u7531\u4e8e\u6bcf\u76f8\u90bb\u7684\u4e24\u5c42\u7684\u8282\u70b9\u90fd\u662f\u5168\u90e8\u8fde\u63a5\u7684\uff0c\u56e0\u6b64\u5728\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0c\u4e5f\u53eb\u505a\u5168\u8fde\u63a5\u795e\u7ecf\u7f51\u7edc\u6216\u591a\u5c42\u611f\u77e5\u673a\uff08Multi-Layer Perceptron, MLP\uff09\u3002<\/p>\n<p>\u56fe15\u53ea\u662f\u663e\u793a\u4e86<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image151.png\" alt=\"img\" \/>\u7684\u51fd\u6570\u7684\u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u6784\u3002\u5bf9\u4e8e\u4e00\u822c\u7684<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image152.png\" alt=\"img\" \/>\u7684\u5411\u91cf\u503c\u51fd\u6570\uff0c\u53ea\u8981\u5c06\u6700\u540e\u8f93\u51fa\u5c42\u591a\u51e0\u4e2a\u8282\u70b9\u5373\u53ef\uff0c\u5373\uff0c\u6bcf\u4e2a\u7ef4\u5ea6\u5206\u91cf\u90fd\u662f\u4e00\u4e2a<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image151.png\" alt=\"img\" \/>\u7684\u51fd\u6570\uff0c\u5171\u4eab\u4e86\u524d\u9762\u7684\u6240\u6709\u7f51\u7edc\u5c42\u7ed3\u6784\u3002<\/p>\n<p>\u6bcf\u4e2a\u9690\u5c42\u7684\u8f93\u51fa<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image153.png\" alt=\"img\" \/> \u90fd\u53ef\u4ee5\u770b\u6210\u8f93\u5165\u6570\u636e<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image154.png\" alt=\"img\" \/>\u5728\u4e0d\u540c\u7ef4\u6570\u7a7a\u95f4<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image155.png\" alt=\"img\" \/>\u4e0b\u7684 \u201c\u7279\u5f81\u201d\u3002<\/p>\n<p>\u6ce8\u610f\u4e0d\u8981\u5728\u8f93\u51fa\u5c42\u4f7f\u7528\u6fc0\u6d3b\u51fd\u6570\u3002\u56e0\u4e3a\u6700\u540e\u7684\u8f93\u51fa\u5c31\u662f\u90a3\u4e9b\u57fa\u51fd\u6570\u7684\u7ebf\u6027\u7ec4\u5408\u8868\u8fbe\u5373\u53ef\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u5f62\u5f0f\u4e0a\u770b\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u4e00\u4e2a\u591a\u5c42\u590d\u5408\u51fd\u6570\u3002\u53ef\u4ee5\u8bc1\u660e\uff08Kolmogorov\u2013Arnold\u8868\u793a\u5b9a\u7406\uff09\uff0c\u4efb\u610f\u4e00\u4e2a\u591a\u5143\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u6210\u82e5\u5e72\u4e2a\u5355\u53d8\u91cf\u51fd\u6570\u7684\u590d\u5408\uff08\u4e8b\u5b9e\u4e0a\uff0c\u53ea\u9700\u8981\u4e09\u5c42\u7f51\u7edc\u5373\u53ef\uff09\u3002\u8fd9\u4e3a\u4f7f\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7528\u6765\u903c\u8fd1\u4efb\u610f\u9ad8\u7ef4\u51fd\u6570\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\u3002\u4f46\u9057\u61be\u7684\u662f\uff0c\u8be5\u5b9a\u7406\u53ea\u8bc1\u660e\u4e86\u590d\u5408\u51fd\u6570\u903c\u8fd1\u4efb\u610f\u51fd\u6570\u7684\u5b58\u5728\u6027\uff0c\u4f46\u5177\u4f53\u4f7f\u7528\u4ec0\u4e48\u6837\u7684\u51fd\u6570\u672a\u53ef\u77e5\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image156.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe15. \u591a\u5143\uff08\u591a\u53d8\u91cf\uff09\u51fd\u6570\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e5f\u80fd\u5f88\u5f3a\u5730\u8868\u8fbe<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image064.png\" alt=\"img\" \/>\u4e2d\u7684\u4efb\u610f\u7684\u51fd\u6570\u3002\u4f46\u5728\u5177\u4f53\u5e94\u7528\u4e2d\uff0c\u9009\u7528\u591a\u5c11\u4e2a\u9690\u5c42\uff0c\u6bcf\u4e00\u9690\u5c42\u9009\u7528\u591a\u5c11\u8282\u70b9\uff0c\u8fd9\u4e9b\u90fd\u662f\u9700\u8981\u6839\u636e\u635f\u5931\u51fd\u6570\u7684\u8fdb\u884c\u4e0d\u65ad\u8c03\u8bd5\u7684\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u4e5f\u79f0\u4e3a\u201c\u8c03\u53c2\u201d\u3002\u53e6\u5916\uff0c\u4ece\u8fd9\u4e2a\u89c2\u70b9\u53ef\u4ee5\u5bb9\u6613\u7406\u89e3\u5404\u79cd\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u5de5\u4f5c\u673a\u5236\uff0c\u5305\u62ec\u4e00\u822c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3001\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff08CNN\uff09\u3001RBF\u795e\u7ecf\u7f51\u7edc\u3001ELM\u7b49\u3002<\/p>\n<h2><strong>\u516b\u3001<\/strong>  <strong>\u6df1\u5165\u7406\u89e3\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc<\/strong><\/h2>\n<p>8.1.      \u6fc0\u6d3b\u51fd\u6570<\/p>\n<p>\u75317.4\u8282\u4e2d\u7684\u4e07\u80fd\u903c\u8fd1\u5b9a\u7406\u53ef\u77e5\uff0c\u6fc0\u6d3b\u51fd\u6570\u7684\u9009\u62e9\u53ef\u4ee5\u5f88\u591a\u79cd\u3002\u5e38\u7528\u7684\u6fc0\u6d3b\u51fd\u6570\u5982\u56fe16\u6240\u793a\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image157.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe16. \u5e38\u7528\u7684\u6fc0\u6d3b\u51fd\u6570\u3002<\/p>\n<p>\u5728\u65e9\u671f\uff0cSigmoid\u51fd\u6570\u548ctanh\u51fd\u6570\u662f\u4eba\u4eec\u7ecf\u5e38\u4f7f\u7528\u7684\u6fc0\u6d3b\u51fd\u6570\u3002\u8fd1\u5e74\u6765\uff0c\u968f\u7740\u795e\u7ecf\u7f51\u7edc\u7684\u9690\u5c42\u4e0d\u65ad\u589e\u52a0\u540e\uff0c\u4eba\u4eec\u504f\u5411\u4e8e\u4f7f\u7528ReLU\u51fd\u6570\u4f5c\u4e3a\u6fc0\u6d3b\u51fd\u6570\uff0c\u8fd9\u662f\u56e0\u4e3aReLU\u51fd\u6570\u7684\u5728x\u8f74\u6b63\u5411\u7684\u5bfc\u6570\u662f1\uff0c\u4e0d\u5bb9\u6613\u4ea7\u751f\u68af\u5ea6\u6d88\u5931\u95ee\u9898\uff08\u89c18.3\u8282\uff09\u3002\u8fd9\u91cc\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u5982\u679c\u4f7f\u7528ReLU\u51fd\u6570\u4f5c\u4e3a\u6fc0\u6d3b\u51fd\u6570\uff0c\u5219\u6700\u540e\u751f\u6210\u7684\u62df\u5408\u51fd\u6570\u4e3a\u5206\u7247\u7ebf\u6027\u51fd\u6570\u3002<\/p>\n<p>\u5173\u4e8e\u6fc0\u6d3b\u51fd\u6570\u7684\u7406\u89e3\u548c\u8ba8\u8bba\uff0c\u673a\u5668\u5b66\u4e60\u9886\u57df\u53ca\u4e92\u8054\u7f51\u4e0a\u6709\u5f88\u591a\u6587\u7ae0\u8fdb\u884c\u8fc7\u89e3\u91ca\uff0c\u90fd\u662f\u89e3\u91ca\u4e3a\u201c\u6fc0\u6d3b\u51fd\u6570\u7684\u4e3b\u8981\u4f5c\u7528\u662f\u63d0\u4f9b\u7f51\u7edc\u7684\u975e\u7ebf\u6027\u5efa\u6a21\u80fd\u529b\uff0c\u63d0\u4f9b\u4e86\u5206\u5c42\u7684\u975e\u7ebf\u6027\u6620\u5c04\u5b66\u4e60\u80fd\u529b\u201d\u7b49\u7b49\u3002\u6211\u4eec\u4ece\u903c\u8fd1\u8bba\u7684\u89d2\u5ea6\uff0c\u5c06\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\u7406\u89e3\u4e3a\u62df\u5408\u51fd\u6570\u7684\u201c\u57fa\u51fd\u6570\u201d\u751f\u6210\u5668\uff08\u5982\u679c\u6fc0\u6d3b\u51fd\u6570\u4e3a\u7ebf\u6027\u7684\uff0c\u5219\u65e0\u6cd5\u751f\u6210\u8868\u8fbe\u975e\u7ebf\u6027\u51fd\u6570\u7684\u57fa\uff01\uff09\uff0c\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u5728\u5b66\u4e60\u8fd9\u4e9b\u57fa\u51fd\u6570\uff0c\u8fd9\u662f\u4e00\u79cd\u5168\u65b0\u7684\u89c2\u70b9\uff0c\u4e5f\u662f\u975e\u5e38\u5bb9\u6613\u7406\u89e3\u7684\u3002<\/p>\n<p>8.2.      \u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\uff08BP\u4f18\u5316\u7b97\u6cd5\uff09<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u770b\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u4e00\u4e2a\u591a\u5c42\u590d\u5408\u51fd\u6570\u3002\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u8fd9\u4e2a\u590d\u5408\u51fd\u6570\u7684\u597d\u574f\u4f9d\u8d56\u4e8e\u5bf9\u76ee\u6807\u51fd\u6570\u6700\u5927\u5316\u6216\u8005\u6700\u5c0f\u5316\u7684\u8fc7\u7a0b\uff0c\u6211\u4eec\u5e38\u5e38\u628a\u6700\u5c0f\u5316\u7684\u76ee\u6807\u51fd\u6570\u79f0\u4e3a\u635f\u5931\u51fd\u6570\uff08Loss function\uff09\uff0c\u5b83\u4e3b\u8981\u7528\u4e8e\u8861\u91cf\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff08\u6b64\u5904\u4e3a\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff09\u7684\u9884\u6d4b\u80fd\u529b\u3002\u5e38\u89c1\u7684\u635f\u5931\u51fd\u6570\u6709\u5747\u65b9\u8bef\u5dee\uff08L2\u8bef\u5dee\uff09\u3001\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee\uff08L1\u8bef\u5dee\uff09\u3001\u5206\u4f4d\u6570\u635f\u5931\u3001\u4ea4\u53c9\u71b5\u3001\u5bf9\u6bd4\u635f\u5931\u7b49\u3002\u635f\u5931\u51fd\u6570\u7684\u9009\u53d6\u4f9d\u8d56\u4e8e\u53c2\u6570\u7684\u6570\u91cf\u3001\u5f02\u5e38\u503c\u3001\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u3001\u68af\u5ea6\u4e0b\u964d\u7684\u6548\u7387\u3001\u5bfc\u6570\u6c42\u53d6\u7684\u96be\u6613\u548c\u9884\u6d4b\u7684\u7f6e\u4fe1\u5ea6\u7b49\u82e5\u5e72\u65b9\u9762\u3002\u8fd9\u91cc\u5c31\u4e0d\u5c55\u5f00\u8ba8\u8bba\u3002<\/p>\n<p>\u7ed9\u5b9a\u4e86\u4e00\u6279\u8bad\u7ec3\u6570\u636e\uff0c\u8ba1\u7b97\u795e\u7ecf\u7f51\u7edc\u7684\u95ee\u9898\u5c31\u662f\u901a\u8fc7\u6781\u5c0f\u5316\u635f\u5931\u51fd\u6570\u6765\u627e\u5230\u7f51\u7edc\u4e2d\u7684\u6240\u6709\u6743\u503c\u53c2\u6570\uff08\u5305\u62ec\u504f\u7f6e\u53c2\u6570\uff09\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u672c\u8d28\u4e0a\u5c31\u662f\u5229\u7528\u8fd9\u4e2a\u795e\u7ecf\u7f51\u7edc\u51fd\u6570\u6765\u62df\u5408\u8fd9\u4e9b\u6570\u636e\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u4e5f\u79f0\u4e3a\u201c\u8bad\u7ec3\u201d\u6216\u201c\u5b66\u4e60\u201d\u3002<\/p>\n<p>\u8bef\u5dee\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\uff08Error Back Propagation\uff0cBP\uff09\u662f\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u65f6\u91c7\u7528\u7684\u4e00\u79cd\u901a\u7528\u65b9\u6cd5\u3002\u672c\u8d28\u662f\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6cd5\u3002\u6700\u65e9\u89c1\u4e8e\u5982\u4e0b\u8bba\u6587\uff1a<\/p>\n<p>[8-1] David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams. Learning internal representations by back-propagating errors. Nature, 323(99): 533-536, 1986.<\/p>\n<p>\u7531\u4e8e\u6574\u4e2a\u7f51\u7edc\u662f\u4e00\u4e2a\u590d\u5408\u51fd\u6570\uff0c\u56e0\u6b64\uff0c\u8bad\u7ec3\u7684\u8fc7\u7a0b\u5c31\u662f\u4e0d\u65ad\u5730\u5e94\u7528\u201c\u590d\u5408\u51fd\u6570\u6c42\u5bfc\u201d\uff08\u94fe\u5f0f\u6cd5\u5219\uff09\u53ca\u201c\u68af\u5ea6\u4e0b\u964d\u6cd5\u201d\u3002\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u4ece\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u51fa\u5c42\u5f00\u59cb\uff0c\u5229\u7528\u9012\u63a8\u516c\u5f0f\u6839\u636e\u540e\u4e00\u5c42\u7684\u8bef\u5dee\u8ba1\u7b97\u672c\u5c42\u7684\u8bef\u5dee\uff0c\u901a\u8fc7\u8bef\u5dee\u8ba1\u7b97\u672c\u5c42\u53c2\u6570\u7684\u68af\u5ea6\u503c\uff0c\u7136\u540e\u5c06\u5dee\u9879\u4f20\u64ad\u5230\u524d\u4e00\u5c42\u3002\u7136\u540e\u6839\u636e\u8fd9\u4e9b\u8bef\u5dee\u6765\u66f4\u65b0\u8fd9\u4e9b\u7cfb\u6570\u53c2\u6570\u3002<\/p>\n<p>\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u68af\u5ea6\u4e0b\u964d\u6cd5\u5e76\u4e0d\u662f\u552f\u4e00\u7684\u4f18\u5316\u65b9\u6cd5\u3002\u4e5f\u6709\u4e0d\u5c11\u4eba\u4f7f\u7528\u5176\u4ed6\u4f18\u5316\u65b9\u6cd5\uff0c\u6bd4\u5982ADMM\u65b9\u6cd5\uff0c\u6765\u4f5c\u4e3a\u4f18\u5316\u5668\u4f18\u5316\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6c42\u89e3\u3002<\/p>\n<p>8.3.      \u4ec0\u4e48\u662f\u597d\u7684\u6fc0\u6d3b\u51fd\u6570\uff1f<\/p>\n<p>\u7531\u4e07\u80fd\u903c\u8fd1\u5b9a\u7406\u53ef\u77e5\uff0c\u53ea\u8981\u7f51\u7edc\u89c4\u6a21\u8bbe\u8ba1\u5f97\u5f53\uff0c\u4f7f\u7528\u975e\u7ebf\u6027\u51fd\u6570\u4f5c\u4e3a\u6fc0\u6d3b\u51fd\u6570\uff08\u6bd4\u59828.1\u8282\u4e2d\u5e38\u7528\u7684\u6fc0\u6d3b\u51fd\u6570\uff09\u7684\u903c\u8fd1\u80fd\u529b\u90fd\u80fd\u591f\u5f97\u5230\u4fdd\u8bc1\u3002<\/p>\n<p>\u7136\u540e\uff0c\u7531\u4e0a\u4e00\u8282\u7684\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u53ef\u77e5\uff0c\u7b97\u6cd5\u8fc7\u7a0b\u4e2d\u8ba1\u7b97\u8bef\u5dee\u9879\u65f6\u6bcf\u4e00\u5c42\u90fd\u8981\u4e58\u4ee5\u672c\u5c42\u6fc0\u6d3b\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u56e0\u6b64\uff0c\u4f1a\u53d1\u751f\u5f88\u591a\u6b21\u7684\u5bfc\u6570\u8fde\u4e58\u3002\u5982\u679c\u6fc0\u6d3b\u51fd\u6570\u7684\u5bfc\u6570\u7684\u7edd\u5bf9\u503c\u5c0f\u4e8e1\uff0c\u591a\u6b21\u8fde\u4e58\u4e4b\u540e\u8bef\u5dee\u9879\u5f88\u5feb\u4f1a\u8870\u51cf\u5230\u63a5\u8fd1\u4e8e0\uff1b\u800c\u53c2\u6570\u7684\u68af\u5ea6\u503c\u7531\u8bef\u5dee\u9879\u8ba1\u7b97\u5f97\u5230\uff0c\u4ece\u800c\u5bfc\u81f4\u524d\u9762\u5c42\u7684\u6743\u91cd\u68af\u5ea6\u63a5\u8fd1\u4e8e0\uff0c\u53c2\u6570\u4e0d\u80fd\u5f97\u5230\u6709\u6548\u66f4\u65b0\uff0c\u8fd9\u79f0\u4e3a\u201c\u68af\u5ea6\u6d88\u5931\u201d\u95ee\u9898\u3002\u4e0e\u4e4b\u76f8\u53cd\uff0c\u5982\u679c\u6fc0\u6d3b\u51fd\u6570\u5bfc\u6570\u7684\u7edd\u5bf9\u503c\u5927\u4e8e1\uff0c\u591a\u6b21\u8fde\u4e58\u540e\u6743\u91cd\u503c\u4f1a\u8d8b\u5411\u4e8e\u975e\u5e38\u5927\u7684\u6570\uff0c\u8fd9\u79f0\u4e3a\u201c\u68af\u5ea6\u7206\u70b8\u201d\u3002\u957f\u671f\u4ee5\u6765\uff0c\u8fd9\u4e24\u4e2a\u95ee\u9898\u4e00\u76f4\u56f0\u6270\u795e\u7ecf\u7f51\u7edc\u5c42\u6b21\u65e0\u6cd5\u53d8\u5f97\u5f88\u6df1\u3002<\/p>\n<p>\u6700\u8fd1\u51e0\u5e74\uff0cReLU\u51fd\u6570\u88ab\u7ecf\u5e38\u4f7f\u7528\u4f5c\u4e3a\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6fc0\u6d3b\u51fd\u6570\u3002\u6709\u4e24\u4e2a\u4e3b\u8981\u7406\u7531\uff1a<\/p>\n<p>\\1)   \u8be5\u51fd\u6570\u7684\u5bfc\u6570\u4e3asgn\uff08\u5ffd\u7565\u57280\u5904\u4e0d\u53ef\u5bfc\u7684\u60c5\u5f62\uff09\uff0c\u8ba1\u7b97\u7b80\u5355\uff0c\u5728\u6b63\u534a\u8f74\u5bfc\u6570\u4e3a1\uff0c\u6709\u6548\u7684\u7f13\u89e3\u4e86\u68af\u5ea6\u6d88\u5931\u95ee\u9898\uff1b<\/p>\n<p>\\2)   \u867d\u7136\u5b83\u662f\u4e00\u4e2a\u5206\u6bb5\u7ebf\u6027\u51fd\u6570\uff0c\u4f46\u5b83\u5177\u6709\u975e\u7ebf\u6027\u903c\u8fd1\u80fd\u529b\uff1b\u4f7f\u7528ReLU\u6fc0\u6d3b\u51fd\u6570\u7684\u6df1\u5ea6\u7f51\u7edc\u7684\u672c\u8d28\u662f\u7528\u5206\u6bb5\uff08\u5206\u7247\uff09\u7ebf\u6027\u51fd\u6570\uff08\u8d85\u5e73\u9762\uff09\u53bb\u903c\u8fd1\u76ee\u6807\u3002<\/p>\n<p>\u540e\u6765\uff0c\u4eba\u4eec\u5728ReLU\u7684\u57fa\u7840\u4e0a\u53c8\u6539\u8fdb\u5f97\u5230\u5404\u79cd\u5176\u4ed6\u5f62\u5f0f\u7684\u6fc0\u6d3b\u51fd\u6570\uff0c\u5305\u62ecELU\u3001PReLU\u7b49\u3002<\/p>\n<p>8.4.      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space\uff09\u4e0a\u89c2\u6d4b\u7684\uff0c\u53ef\u80fd\u6570\u636e\u7684\u7ef4\u6570\u975e\u5e38\u9ad8\uff08\u6bd4\u59821000x1000\u7684\u56fe\u50cf\u6309\u7167\u50cf\u7d20\u4e2a\u6570\u7684\u7ef4\u6570\u8fbe\u5230100\u4e07\u7ef4\uff09\u3002\u4f46\u8fd9\u4e9b\u6570\u636e\u5e76\u4e0d\u4f1a\u5145\u6ee1\u6574\u4e2a\u9ad8\u7ef4\u7a7a\u95f4\uff0c\u4f1a\u5177\u6709\u4f4e\u7ef4\u7684\u7ed3\u6784\uff08\u79f0\u4e3a\u672c\u5f81\u7ef4\u6570\uff09\uff0c\u5373\u6570\u636e\u843d\u5728\u4e00\u4e2a\u4f4e\u7ef4\u5b50\u7a7a\u95f4\uff08\u6216\u4f4e\u7ef4\u6d41\u5f62\uff09\u4e0a\uff0c\u5e76\u5448\u73b0\u4e00\u5b9a\u7684\u6982\u7387\u5206\u5e03\u3002\u4ece\u6570\u636e\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u4e00\u4e2a\u5d4c\u5165\u5230\u9ad8\u7ef4\u7a7a\u95f4\u7684\u4f4e\u7ef4\u6d41\u5f62\u672c\u8d28\u4e0a\u5c31\u662f\u4e00\u4e2a\u53c2\u6570\u66f2\u9762\uff0c\u53c2\u6570\u57df\u662f\u90a3\u4e2a\u4f4e\u7ef4\u7a7a\u95f4\u3002\u56e0\u6b64\uff0c\u5c06\u9ad8\u7ef4\u6570\u636e\u53c2\u6570\u5316\u5230\u4f4e\u7ef4\u7684\u7a7a\u95f4\u662f\u53ef\u884c\u7684\u3002<\/p>\n<p>\u8fd9\u91cc\u4e5f\u51fa\u73b0\u4e86\u4e24\u4e2a\u7ea0\u7ed3\u7684\u95ee\u9898\u3002<\/p>\n<p>\u7b2c\u4e00\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u5b9e\u9645\u6570\u636e\u62df\u5408\u95ee\u9898\uff0c\u5e94\u8be5\u8bbe\u7f6e\u591a\u5c11\u4e2a\u9690\u5c42\uff1f<\/p>\n<p>\u7b2c\u4e8c\uff0c\u6bcf\u4e2a\u9690\u5c42\u5e94\u8be5\u8bbe\u7f6e\u591a\u5c11\u4e2a\u8282\u70b9\uff08\u8be5\u9690\u5c42\u7684\u7ef4\u6570\uff09\uff1f<\/p>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0c\u9690\u5c42\u7684\u5c42\u6570\u79f0\u4e3a\u7f51\u7edc\u7684\u6df1\u5ea6\uff0c\u9690\u5c42\u7684\u7ef4\u6570\u6210\u4e3a\u7f51\u7edc\u7684\u5bbd\u5ea6\u3002\u5bf9\u4e8e\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\uff0c\u5230\u5e95\u662f\u8d8a\u6df1\u8d8a\u597d\uff0c\u8fd8\u662f\u8d8a\u5bbd\u8d8a\u597d\uff1f<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u6765\u770b\uff0c\u7f51\u7edc\u8d8a\u6df1\uff0c\u8868\u793a\u4e00\u4e2a\u590d\u6742\u7684\u51fd\u6570\u53ef\u4ee5\u7ecf\u8fc7\u591a\u6b21\u53c2\u6570\u5316\u7684\u53d8\u6362\uff0c\u6620\u5c04\u5230\u6700\u7ec8\u7684\u76ee\u6807\u3002\u8fd9\u4e2a\u662f\u5408\u7406\u7684\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u6bd4\u5982\u6211\u4eec\u60f3\u5c06\u4e00\u4e2a\u4e09\u7ef4\u7f51\u683c\u66f2\u9762\u53c2\u6570\u5316\u5230\u4e00\u4e2a\u5e73\u9762\uff0c\u5982\u679c\u8fd9\u4e2a\u8f93\u5165\u7684\u66f2\u9762\u6bd4\u8f83\u590d\u6742\uff0c\u5f00\u53e3\uff08\u53c2\u6570\u5316\u8fb9\u754c\uff09\u5f88\u5c0f\uff0c\u5219\u8981\u5c06\u66f2\u9762\u4e00\u6b21\u6027\u5c55\u5f00\uff08<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image084.png\" alt=\"img\" \/>\u5230<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image077.png\" alt=\"img\" \/>\u7684\u6620\u5c04\uff09\u6bd4\u8f83\u56f0\u96be\u3002\u6b64\u65f6\uff0c\u53ef\u4ee5\u591a\u8fdb\u884c\u51e0\u6b21\u4ece<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image084.png\" alt=\"img\" \/>\u5230<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image084.png\" alt=\"img\" \/>\u7684\u6620\u5c04\uff0c\u5c06\u66f2\u9762\u5148\u5728<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image084.png\" alt=\"img\" \/>\u6162\u6162\u5f20\u5f00\uff0c\u6bcf\u6b21\u5f20\u5f00\u7684\u6620\u5c04\u6bd4\u8f83\u5bb9\u6613\u8868\u8fbe\u548c\u8ba1\u7b97\u3002\u6700\u540e\u518d\u6620\u5c04\u5230<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image077.png\" alt=\"img\" \/>\u4e0a\u5c31\u76f8\u5bf9\u5bb9\u6613\u4e86\uff0c\u5f53\u7136\u8fd8\u53ef\u8fdb\u884c\u591a\u6b21\u4ece<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image077.png\" alt=\"img\" \/>\u5230<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image077.png\" alt=\"img\" \/>\u7684\u6620\u5c04\uff0c\u751f\u6210\u66f4\u597d\u7684\u53c2\u6570\u5316\u3002\u6ce8\u610f\u5176\u4e2d\u4efb\u4f55\u4e00\u4e2a\u6620\u5c04\u90fd\u53ef\u4ee5\u662f\u7528\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u6765\u8868\u8fbe\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image158.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe17. \u5e26\u6709\u7279\u5f81\u7684\u66f2\u9762\u7684\u62df\u5408\u3002(a) \u539f\u59cb\u8f93\u5165\u4e09\u7ef4\u6570\u636e\uff1b(b) \u4e3a(a)\u7684\u7b80\u5355\u53c2\u6570\u5316\uff08Floater\u53c2\u6570\u5316\uff09\uff1b(c) \u4e3a\u4f18\u5316\u8fc7\u540e\u7684\u53c2\u6570\u5316\uff1b(d) \u6700\u540e\u7684\u62df\u5408\u66f2\u9762\u3002<\/p>\n<p>\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0c\u6211\u4eec\u9488\u5bf9\u66f2\u9762\u5c55\u5f00\u53ca\u62df\u5408\u95ee\u9898\uff0c\u5728\u5982\u4e0b\u7684\u5de5\u4f5c\u4e2d\u7528\u5230\u4e86\u8fd9\u79cd\u601d\u60f3\u3002<\/p>\n<p>[8-2] Linlin Xu, Ruimin Wang, Zhouwang Yang, Jiansong Deng, Falai Chen, Ligang Liu. Surface Approximation via Sparse Representation and Parameterization Optimization. Computer-Aided Design (Proc. SPM), 78: 179-187, 2016.<\/p>\n<p>\u5982\u56fe17\u6240\u793a\uff0c(a) \u4e3a\u4e00\u4e2a\u5e26\u6709\u5c16\u9510\u7279\u5f81\u7684\u8f93\u5165\u70b9\u4e91\uff0c\u5982\u679c\u5c06\u5176\u7b80\u5355\u53c2\u6570\u5316\u4e3a(b)\uff0c\u5728\u5176\u4e0a\u6784\u5efa\u7684\u62df\u5408\u66f2\u9762\u5f88\u96be\u8868\u73b0\u66f2\u9762\u7684\u5c16\u9510\u7279\u5f81\u3002\u8fd9\u65f6\u6211\u4eec\u5bf9(b)\u4e2d\u7684\u53c2\u6570\u5316\u518d\u505a\u4e00\u4e2a\u6620\u5c04\uff08\u4f18\u5316\uff09\u4e3a(c)\uff0c\u8fd9\u65f6\u5728\u5176\u4e0a\u505a\u7684\u62df\u5408\u66f2\u9762\u5219\u80fd\u5f88\u597d\u5730\u8868\u73b0\u51fa\u5c16\u9510\u7279\u5f81\u3002\u6ce8\u610f\uff0c\u8fd9\u91cc\u751f\u6210\u62df\u5408\u66f2\u9762\u7684\u57fa\u51fd\u6570\u4e2d\u6211\u4eec\u91c7\u7528\u4e86\u975e\u5149\u6ed1\u57fa\u51fd\u6570\uff08\u91c7\u7528\u975e\u5149\u6ed1\u57fa\u51fd\u6570\u6765\u8868\u73b0\u66f2\u9762\u7279\u5f81\u7684\u601d\u60f3\u9996\u6b21\u5728\u6211\u4eec\u7684\u5982\u4e0b\u8bba\u6587\u4e2d\u6240\u91c7\u7528\uff09\u3002\u56e0\u6b64\uff0c\u4e0a\u8ff0\u5de5\u4f5c\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u4f7f\u75285\u5c42\u795e\u7ecf\u7f51\u7edc\uff083\u4e2a\u9690\u5c42\uff09\u6765\u4f18\u5316\u62df\u5408\u66f2\u9762\u3002<\/p>\n<p>[8-3] Ruimin Wang, Ligang Liu, Zhouwang Yang, Kang Wang, Wen Shan, Jiansong Deng, Falai Chen. Construction of Manifolds via Compatible Sparse Representations. ACM Transactions on Graphics, 35(2), Article 14: 1-10, 2016.<\/p>\n<p>\u8fd9\u91cc\u987a\u4fbf\u63d0\u4e00\u4e0b\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0c\u6700\u8fd1\u4e00\u4e9b\u5e74\u6709\u4e0d\u5c11\u5de5\u4f5c\u5728\u505a\u66f2\u9762\u53c2\u6570\u5316\u7684\u4f18\u5316\u5de5\u4f5c\uff08\u6bd4\u5982\u6ee1\u8db3\u65e0\u7ffb\u8f6c\u3001\u4f4e\u626d\u66f2\u7b49\u7ea6\u675f\uff09\u3002\u4ece\u673a\u5668\u5b66\u4e60\u7684\u89c2\u70b9\u6765\u770b\uff0c\u5c31\u662f\u5728\u505a\u66f4\u591a\u7684\u53c2\u6570\u6620\u5c04\u7684\u4f18\u5316\u8ba1\u7b97\u3002\u5f53\u7136\uff0c\u8fd9\u4e9b\u5de5\u4f5c\u5e76\u4e0d\u80fd\u7b80\u5355\u5730\u770b\u6210\u4e00\u4e2a\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u6765\u505a\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u5bf9\u53c2\u6570\u5316\u7684\u95ee\u9898\uff0c\u6211\u4eec\u662f\u77e5\u9053\u66f2\u9762\uff08\u6240\u6709\u6570\u636e\uff09\u7684\u6574\u4f53\u7ed3\u6784\u7684\uff0c\u800c\u4e0d\u53ea\u662f\u4e00\u4e9b\u79bb\u6563\u7684\u91c7\u6837\u70b9\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u505a\u53c2\u6570\u5316\u4f18\u5316\u7684\u65f6\u5019\uff0c\u6211\u4eec\u53ef\u4ee5\u5145\u5206\u5229\u7528\u66f2\u9762\u7684\u6574\u4f53\u7ed3\u6784\u6765\u5f97\u5230\u4e00\u4e9b\u51e0\u4f55\u5ea6\u91cf\u6765\u6ee1\u8db3\u5404\u79cd\u7ea6\u675f\uff0c\u800c\u8fd9\u4e9b\u662f\u795e\u7ecf\u7f51\u7edc\u4f18\u5316\u6240\u505a\u4e0d\u5230\u7684\uff01<\/p>\n<p>\u603b\u4e4b\uff0c\u5bf9\u4e8e\u7b2c\u4e00\u4e2a\u95ee\u9898\uff0c\u9690\u5c42\u8d8a\u591a\uff0c\u8868\u793a\u7f51\u7edc\u8d8a\u6df1\uff0c\u786e\u5b9e\u4f1a\u4f7f\u5f97\u6700\u540e\u7684\u6620\u5c04\u5e26\u6765\u66f4\u597d\u7684\u8868\u73b0\u3002\u5176\u6570\u5b66\u672c\u8d28\u662f\u5c06\u8f93\u5165\u6570\u636e\u4e0d\u65ad\u5728\u4e0d\u540c\u7684\u7a7a\u95f4\u4e2d\u8fdb\u884c\u53c2\u6570\u5316\u6620\u5c04\u3002\u6700\u540e\u5f97\u5230\u7684\u6620\u5c04\uff08\u53ef\u80fd\u975e\u5e38\u590d\u6742\u7684\u6620\u5c04\uff09\u8868\u8fbe\u4e3a\u82e5\u5e72\u4e2a\u76f8\u5bf9\u7b80\u5355\u6620\u5c04\u7684\u590d\u5408\u3002\u5bf9\u4e8e\u591a\u9690\u5c42\u7684\u89e3\u91ca\u548c\u8ba8\u8bba\uff0c\u673a\u5668\u5b66\u4e60\u9886\u57df\u53ca\u7f51\u4e0a\u6709\u5f88\u591a\u6587\u7ae0\u8fdb\u884c\u8fc7\u89e3\u91ca\uff0c\u5927\u90e8\u5206\u90fd\u89e3\u91ca\u4e3a\u201c\u63d0\u53d6\u6570\u636e\u7684\u7279\u5f81\u201d\u7b49\u7b49\u3002\u6211\u4eec\u4ece\u903c\u8fd1\u8bba\u7684\u89d2\u5ea6\uff08\u7ed3\u5408\u4e09\u7ef4\u66f2\u9762\u62df\u5408\u7684\u4f8b\u5b50\uff09\uff0c\u5c06\u591a\u9690\u5c42\u4f18\u5316\u770b\u6210\u6570\u636e\u5728\u4e0d\u540c\u7ef4\u6570\u7a7a\u95f4\u7684\u53c2\u6570\u5316\uff0c\u662f\u975e\u5e38\u5bb9\u6613\u76f4\u89c2\u7406\u89e3\u7684\u3002<\/p>\n<p>\u5bf9\u7b2c\u4e8c\u4e2a\u95ee\u9898\uff0c\u6bcf\u4e2a\u9690\u5c42\u7684\u5177\u4f53\u7684\u8282\u70b9\u6570\u6216\u7ef4\u6570\uff0c\u8be5\u5982\u4f55\u8bbe\u7f6e\u5462\uff1f\u5bf9\u4e8e\u4e00\u822c\u7684\u6570\u636e\u8fd9\u4e2a\u5c31\u5f88\u96be\u76f4\u89c2\u786e\u5b9a\u4e86\uff0c\u4e00\u822c\u8981\u6839\u636e\u7ecf\u9a8c\u3002\u5f53\u7136\uff0c\u4e5f\u6709\u4e00\u4e9b\u529e\u6cd5\u6765\u8fdb\u884c\u6307\u5bfc\uff0c\u6211\u4eec\u5c06\u5728\u4e0b\u4e00\u8282\u4e2d\u7406\u89e3\u3002<\/p>\n<p>8.5.      \u6d41\u5f62\u5b66\u4e60\uff08\u6570\u636e\u964d\u7ef4\uff09\u7b80\u4ecb<\/p>\n<p>\u5bf9\u4e8e\u4e00\u822c\u7684\u6570\u636e\uff0c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u5176\u672c\u5f81\u7ef4\u6570\uff08\u5373\u53c2\u6570\u57df\u7a7a\u95f4\uff09\uff0c\u90a3\u4e48\u6620\u5c04\uff08\u53c2\u6570\u5316\uff09\u5230\u591a\u5c11\u7ef4\u7a7a\u95f4\u662f\u5408\u9002\u7684\u5462\uff1f<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e2a\u4e5f\u662f\u4e2a\u975e\u5e38\u7ea0\u7ed3\u7684\u95ee\u9898\uff01\u8fd9\u4e2a\u95ee\u9898\u5c31\u662f\u5bfb\u6c42\u9ad8\u7ef4\u6570\u636e\u7684\u672c\u5f81\u7ef4\u6570\uff0c\u5728\u673a\u5668\u5b66\u4e60\u9886\u57df\u79f0\u4e3a\u6d41\u5f62\u5b66\u4e60\uff08Manifold learning\uff09\uff0c\u6216\u964d\u7ef4\u95ee\u9898\uff08Dimension reduction\uff09\u3002\u5982\u56fe18\u6240\u793a\uff0c\u6570\u636e\u662f\u5728\u4e09\u7ef4\u7a7a\u95f4\u7ed9\u51fa\u7684\uff08B\uff09\uff0c\u6bcf\u4e2a\u70b9\u662f3\u4e2a\u5750\u6807\uff0c\u770b\u8d77\u6765\u662f\u4e09\u7ef4\u6570\u636e\uff1b\u4f46\u5176\u672c\u8d28\u4e0a\u4f4d\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u7684\u4e00\u5f20\u66f2\u9762\u4e0a\uff0c\u5373\u4e8c\u7ef4\u6d41\u5f62\u66f2\u9762\u4e0a\uff08A\uff09\uff0c\u5176\u672c\u5f81\u7ef4\u6570\u662f2\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u5c06\u5176\u4e00\u4e00\u6620\u5c04\u5230\u5e73\u9762\u4e0a\uff08C\uff09\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image159.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe18. \u6d41\u884c\u5b66\u4e60\u3002\uff08\u56fe\u7247\u6765\u81ea\u8bba\u6587[8-5]\uff09<\/p>\n<p>\u63d0\u5230\u6d41\u5f62\u5b66\u4e60\uff0c\u4e0d\u80fd\u4e0d\u63d0\u5230\u5982\u4e0b\u7684\u4e24\u7bc7\u5f00\u5c71\u4e4b\u4f5c\uff08\u540c\u65f6\u53d1\u5728Science 2000\u7684\u6587\u7ae0\uff09\uff1a<\/p>\n<p>[8-4] Roweis, Sam T and Saul, Lawrence K. Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500). 2000: 2323-2326.<\/p>\n<p>[8-5] Tenenbaum, Joshua B and De Silva, Vin and Langford, John C. A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500). 2000: 2319-2323.<\/p>\n<p>\u6d41\u5f62\u5b66\u4e60\u5728\u672c\u4e16\u7eaa\u521d\u7684\u524d\u4e00\u4e2a\u5341\u5e74\u662f\u4e00\u4e2a\u7814\u7a76\u70ed\u70b9\uff08\u7531\u4e0a\u9762\u4e24\u7bc7Science\u8bba\u6587\u5e26\u8d77\u6765\u7684\uff09\u3002\u81f3\u4eca\u5df2\u53d1\u5c55\u51fa\u4e86\u8bb8\u591a\u65b9\u6cd5\uff0c\u4ece\u7b80\u5355\u7684\u7ebf\u6027\u65b9\u6cd5\uff0c\u6bd4\u5982PCA\uff1b\u5230\u540e\u9762\u7684\u975e\u7ebf\u6027\u65b9\u6cd5\uff0c\u6bd4\u5982\u5c40\u90e8\u7ebf\u6027\u5d4c\u5165\uff08LLE\uff09\uff0c\u7b49\u8ddd\u6620\u5c04\u6cd5\uff08Isomap\uff09\uff0cLaplace\u7279\u5f81\u6620\u5c04\uff0c\u5c40\u90e8\u4fdd\u6295\u5f71\u6cd5\uff08LPP\uff09\u7b49\u3002\u8fd9\u91cc\u4e0d\u8be6\u7ec6\u4ecb\u7ecd\u3002<\/p>\n<p>\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u6b63\u5982\u7b2c6\u8282\u6240\u8bb2\u7684\u4e09\u7ef4\u66f2\u9762\u53c2\u6570\u5316\u7684\u8ba1\u7b97\uff0c\u6211\u4eec\u8ba1\u7b97\u6570\u636e\u7684\u672c\u5f81\u7ef4\u6570\u7684\u65f6\u5019\uff0c\u662f\u9700\u8981\u5229\u7528\u6240\u6709\u6570\u636e\u7684\u4fe1\u606f\u53ca\u5176\u51e0\u4f55\u6216\u62d3\u6251\u7ed3\u6784\u4e00\u8d77\u6765\u5206\u6790\u7684\uff0c\u800c\u4e0d\u80fd\u50cf\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u90a3\u6837\uff0c\u4ec5\u4ec5\u5c06\u6570\u636e\u704c\u5230\u795e\u7ecf\u7f51\u7edc\u4e2d\u53bb\u66f4\u65b0\u6743\u7cfb\u6570\u3002<\/p>\n<p>8.6.      \u7aef\u5bf9\u7aef\u5b66\u4e60\uff08End-to-end learning\uff09<\/p>\n<p>\u5728\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u5f88\u591a\u4efb\u52a1\u7684\u8f93\u5165\u6570\u636e\u7684\u7ef4\u6570\u90fd\u975e\u5e38\u5927\uff0c\u4e0d\u6613\u76f4\u63a5\u5904\u7406\u3002\u5f80\u5f80\u9700\u8981\u5148\u964d\u5230\u5408\u9002\u7684\u7ef4\u6570\uff0c\u7136\u540e\u518d\u9009\u62e9\u5408\u9002\u7684\u9884\u6d4b\u6a21\u578b\u6765\u505a\u62df\u5408\u3002<\/p>\n<p>\u4f20\u7edf\u673a\u5668\u5b66\u4e60\u7684\u6d41\u7a0b\u4e00\u822c\u7531\u4e24\u4e2a\u4e3b\u8981\u7684\u6a21\u5757\u7ec4\u6210\u3002\u7b2c\u4e00\u4e2a\u6a21\u5757\u79f0\u4e3a\u7279\u5f81\u5de5\u7a0b\uff0c\u5c06\u539f\u59cb\u8f93\u5165\u6570\u636e\uff08\u9ad8\u7ef4\u5411\u91cf\uff09\u53d8\u6362\u4e3a\u4e00\u4e2a\u4f4e\u7ef4\u5411\u91cf\uff0c\u5373\uff0c\u7528\u8fd9\u4e2a\u4f4e\u7ef4\u5411\u91cf\u6765\u4f5c\u4e3a\u8868\u8fbe\u8f93\u5165\u6570\u636e\u7684\u7279\u5f81\uff08\u6216\u63cf\u8ff0\u5b50\uff0cfeature or descriptor\uff09\u3002\u4e0d\u540c\u7684\u4eba\u6709\u4e0d\u540c\u7684\u65b9\u6cd5\u6765\u8ba1\u7b97\u8fd9\u4e2a\u4f4e\u7ef4\u7279\u5f81\uff0c\u79f0\u4e3a\u7279\u5f81\u62bd\u53d6\uff08Feature extraction\uff09\uff0c\u5982\u56fe19\u663e\u793a\u4e86\u4e0d\u540c\u7684\u56fe\u50cf\u7279\u5f81\u62bd\u53d6\u65b9\u6cd5\u3002\u5404\u79cd\u8ba1\u7b97\u7684\u7279\u5f81\u90fd\u6709\u4e00\u5b9a\u7684\u5b9e\u7528\u8303\u56f4\uff0c\u56e0\u6b64\uff0c\u6709\u4eba\u5c31\u63d0\u51fa\u5982\u4f55\u9009\u62e9\u6216\u7ec4\u5408\u5404\u79cd\u7279\u5f81\u5f97\u5230\u66f4\u597d\u7684\u7279\u5f81\uff0c\u8fd9\u662f\u7279\u5f81\u5de5\u7a0b\u7684\u53e6\u4e00\u4e2a\u5b50\u95ee\u9898\uff0c\u79f0\u4e3a\u7279\u5f81\u9009\u62e9\uff08Feature selection\uff09\u3002\u9488\u5bf9\u4e09\u7ef4\u5f62\u72b6\u5206\u5272\uff0c\u6211\u4eec\u53d1\u73b0\u5bf9\u4e09\u7ef4\u5c40\u90e8\u5757\u7684\u4f17\u591a\u63cf\u8ff0\u5b50\u5e76\u4e0d\u662f\u4e32\u8054\u8d77\u6765\u4e00\u8d77\u4f7f\u7528\u66f4\u597d\uff0c\u800c\u662f\u9488\u5bf9\u4e0d\u540c\u7684\u5f62\u72b6\u7684\u90e8\u4f4d\u4f7f\u7528\u4e0d\u540c\u7684\u63cf\u8ff0\u5b50\u4f1a\u66f4\u597d\uff0c\u4e8e\u662f\u6211\u4eec\u4f7f\u7528\u7a00\u758f\u9009\u62e9\u7684\u65b9\u6cd5\u6765\u9009\u62e9\u5f62\u72b6\u63cf\u8ff0\u5b50\u7528\u4e8e\u5f62\u72b6\u5206\u5272\uff0c\u8be6\u7ec6\u53ef\u89c1\u5982\u4e0b\u8bba\u6587\u3002<\/p>\n<p>[8-6] Ruizhen Hu, Lubin Fan, Ligang Liu. Co-Segmentation of 3D Shapes via Subspace Clustering. Computer Graphics Forum (Proc. Symposium on Geometry Processing), 31(5): 1703-1713, 2012.<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image160.jpg\" alt=\"1365435491_6508.jpg\" \/><\/p>\n<p>\u56fe19. \u56fe\u50cf\u7684\u5404\u79cd\u7279\u5f81\u62bd\u53d6\u65b9\u6cd5\u3002<\/p>\n<p>\u7531\u4e8e\u8fd9\u79cd\u7279\u5f81\u662f\u901a\u8fc7\u4eba\u4e3a\u8bbe\u8ba1\u7684\u7b97\u6cd5\u6765\u5f97\u5230\u7684\uff0c\u56e0\u6b64\u8fd9\u79cd\u7279\u5f81\u79f0\u4e3a\u4eba\u5de5\u7279\u5f81\uff08Hand-crafted features\uff09\u3002\u4eba\u5de5\u7279\u5f81\u7684\u62bd\u53d6\u9700\u8981\u4eba\u4eec\u5bf9\u8f93\u5165\u6570\u636e\u7684\u8ba4\u77e5\u6216\u8005\u9886\u57df\u77e5\u8bc6\uff08Domain knowledge\uff09\uff0c\u56e0\u6b64\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\u4f1a\u5c40\u9650\u4e8e\u4eba\u7684\u7ecf\u9a8c\u548c\u8ba4\u77e5\u3002<\/p>\n<p>\u7b2c\u4e8c\u4e2a\u6a21\u5757\u79f0\u4e3a\u9884\u6d4b\u6a21\u578b\uff0c\u5373\u9009\u7528\u4ec0\u4e48\u6837\u7684\u9884\u6d4b\u65b9\u6cd5\u6765\u62df\u5408\u7ed9\u5b9a\u7684\u6570\u636e\uff0c\u6211\u4eec\u524d\u9762\u6240\u8bb2\u7684\u62df\u5408\u5c31\u662f\u6307\u8fd9\u4e2a\u8fc7\u7a0b\u3002\u9884\u6d4b\u6a21\u578b\u7684\u76ee\u6807\u5c31\u662f\u5e0c\u671b\u5b66\u4e60\u5230\u7684\u6a21\u578b\u5728\u9884\u6d4b\u672a\u77e5\u76ee\u6807\u65f6\u8d8a\u7cbe\u786e\u8d8a\u597d\u3002\u4e00\u822c\u8981\u8003\u8651\u6a21\u578b\u7684\u590d\u6742\u5ea6\u53ca\u7cbe\u786e\u5ea6\u7b49\u56e0\u7d20\u3002\u5728\u673a\u5668\u5b66\u4e60\u9886\u57df\u6709\u975e\u5e38\u591a\u7684\u65b9\u6cd5\uff0c\u8fd9\u91cc\u4e0d\u4e00\u4e00\u4ecb\u7ecd\u3002<\/p>\n<p>\u4e0a\u8ff0\u4e24\u4e2a\u6a21\u5757\u4e2d\u7684\u6bcf\u4e2a\u6a21\u5757\u90fd\u662f\u4e00\u4e2a\u72ec\u7acb\u7684\u4efb\u52a1\uff0c\u5176\u7ed3\u679c\u7684\u597d\u574f\u4f1a\u5f71\u54cd\u5230\u4e0b\u4e00\u6b65\u9aa4\uff0c\u4ece\u800c\u5f71\u54cd\u6574\u4e2a\u8bad\u7ec3\u7684\u7ed3\u679c\uff0c\u8fd9\u662f\u975e\u7aef\u5230\u7aef\u7684\uff0c\u5982\u56fe20\uff08\u4e0a\uff09\u6240\u793a\u3002<\/p>\n<p>\u7279\u5f81\u63d0\u53d6\u7684\u597d\u574f\u5f02\u5e38\u5173\u952e\uff0c\u751a\u81f3\u6bd4\u9884\u6d4b\u6a21\u578b\u8fd8\u91cd\u8981\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u5bf9\u4e00\u7cfb\u5217\u4eba\u7684\u6570\u636e\u5206\u7c7b\uff0c\u5206\u7c7b\u7ed3\u679c\u662f\u6027\u522b\uff08\u7537\u6216\u5973\uff09\uff0c\u5982\u679c\u4f60\u63d0\u53d6\u7684\u7279\u5f81\u662f\u5934\u53d1\u7684\u989c\u8272\uff0c\u65e0\u8bba\u5206\u7c7b\u7b97\u6cd5\u5982\u4f55\uff0c\u5206\u7c7b\u6548\u679c\u90fd\u4e0d\u4f1a\u597d\uff1b\u5982\u679c\u4f60\u63d0\u53d6\u7684\u7279\u5f81\u662f\u5934\u53d1\u7684\u957f\u77ed\uff0c\u8fd9\u4e2a\u7279\u5f81\u5c31\u4f1a\u597d\u5f88\u591a\uff0c\u4f46\u662f\u8fd8\u662f\u4f1a\u6709\u9519\u8bef\uff1b\u5982\u679c\u4f60\u63d0\u53d6\u4e86\u4e00\u4e2a\u8d85\u5f3a\u7279\u5f81\uff0c\u6bd4\u5982\u67d3\u8272\u4f53\u7684\u6570\u636e\uff0c\u90a3\u4f60\u7684\u5206\u7c7b\u57fa\u672c\u5c31\u4e0d\u4f1a\u9519\u4e86\u3002<\/p>\n<p>\u8fd9\u5c31\u610f\u5473\u7740\uff0c\u7279\u5f81\u9700\u8981\u8db3\u591f\u7684\u7ecf\u9a8c\u53bb\u8bbe\u8ba1\uff0c\u8fd9\u5728\u6570\u636e\u91cf\u8d8a\u6765\u8d8a\u5927\u7684\u60c5\u51b5\u4e0b\u4e5f\u8d8a\u6765\u8d8a\u56f0\u96be\u3002\u4e8e\u662f\u5c31\u51fa\u73b0\u4e86\u7aef\u5230\u7aef\u7684\u7f51\u7edc\uff0c\u7279\u5f81\u53ef\u4ee5\u81ea\u5df1\u53bb\u5b66\u4e60\u3002\u6240\u4ee5\u7279\u5f81\u63d0\u53d6\u8fd9\u4e00\u6b65\u4e5f\u5c31\u878d\u5165\u5230\u7b97\u6cd5\u5f53\u4e2d\uff0c\u4e0d\u9700\u8981\u4eba\u6765\u5e72\u9884\u4e86\u3002\u5373\u4e0d\u9700\u8981\u5c06\u4efb\u52a1\u5206\u4e3a\u591a\u4e2a\u6b65\u9aa4\u5206\u6b65\u53bb\u89e3\u51b3\uff0c\u800c\u662f\u4ece\u8f93\u5165\u7aef\u7684\u6570\u636e\u76f4\u63a5\u5f97\u5230\u8f93\u51fa\u7aef\u7684\u7ed3\u679c\u3002\u524d\u9762\u4ecb\u7ecd\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u4e00\u4e2a\u7aef\u5230\u7aef\u7684\u5b66\u4e60\u65b9\u6cd5\u3002\u5982\u56fe20\uff08\u4e0b\uff09\u6240\u793a\u3002<\/p>\n<p>\u7aef\u5230\u7aef\u5b66\u4e60\u7684\u597d\u5904\u5728\u4e8e\uff0c\u4f7f\u5b66\u4e60\u6a21\u578b\u4ece\u539f\u59cb\u8f93\u5165\u5230\u6700\u7ec8\u8f93\u51fa\uff0c\u76f4\u63a5\u8ba9\u6570\u636e\u201c\u8bf4\u8bdd\u201d\uff0c\u4e0d\u9700\u4eba\u5de5\u8bbe\u8ba1\u7684\u6a21\u5757\uff1b\u7ed9\u6a21\u578b\u66f4\u591a\u53ef\u4ee5\u6839\u636e\u6570\u636e\u81ea\u52a8\u8c03\u8282\u7684\u7a7a\u95f4\uff0c\u589e\u52a0\u6a21\u578b\u7684\u6574\u4f53\u5951\u5408\u5ea6\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image161.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe20. \u975e\u7aef\u5230\u7aef\u7684\u5b66\u4e60\uff08\u4e0a\uff09\u4e0e\u7aef\u5230\u7aef\u7684\u5b66\u4e60\uff08\u4e0b\uff09\u3002<\/p>\n<p>\u4f46\u7aef\u5230\u7aef\u5b66\u4e60\u4e5f\u6709\u4e0d\u8db3\u3002\u7b2c\u4e00\uff0c\u7aef\u5230\u7aef\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u9700\u8981\u5927\u91cf\u7684\u6837\u672c\u6570\u636e\u624d\u80fd\u5de5\u4f5c\u5f97\u5f88\u597d\uff0c\u56e0\u6b64\u5f88\u591a\u516c\u53f8\u90fd\u5728\u82b1\u8d39\u5927\u91cf\u7684\u4eba\u529b\u7269\u529b\u53bb\u751f\u6210\u6807\u6ce8\u6570\u636e\uff08\u4e00\u822c\u901a\u8fc7\u4eba\u5de5\u6807\u6ce8\uff0c\u50ac\u751f\u4e86\u5f88\u591a\u4e13\u95e8\u505a\u6570\u636e\u6807\u6ce8\u7684\u5916\u5305\u516c\u53f8\uff09\uff1b\u7b2c\u4e8c\uff0c\u4eba\u5de5\u8bbe\u8ba1\u7684\u7279\u5f81\u5e76\u4e0d\u662f\u90fd\u4e0d\u80fd\u7528\u7684\uff0c\u6709\u4e9b\u4eba\u5de5\u7279\u5f81\u8fd8\u662f\u80fd\u4ee3\u8868\u7740\u4eba\u7c7b\u667a\u80fd\u7684\uff0c\u662f\u53ef\u4ee5\u7528\u6765\u4f5c\u4e3a\u5408\u7406\u7684\u7279\u5f81\u7684\uff0c\u800c\u7aef\u5230\u7aef\u7684\u5b66\u4e60\u65e0\u6cd5\u7528\u8fd9\u4e9b\u7279\u5f81\u3002\u5f53\u7136\uff0c\u901a\u8fc7\u9002\u5f53\u7684\u6539\u9020\u548c\u7ed3\u5408\uff0c\u4e5f\u53ef\u4ee5\u96c6\u6210\u4eba\u5de5\u7279\u5f81\u5230\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u8fd9\u91cc\u5c31\u4e0d\u5c55\u5f00\u8ba8\u8bba\u3002<\/p>\n<p>8.7.      \u6df1\u5ea6\u5b66\u4e60\u6210\u529f\u7684\u539f\u56e0<\/p>\n<p>\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u7aef\u5230\u7aef\u5b66\u4e60\u5728\u6700\u8fd1\u51e0\u5e74\u53d6\u5f97\u5f88\u5927\u7684\u6210\u529f\uff0c\u88ab\u5927\u91cf\u5e94\u7528\u4e0e\u8ba1\u7b97\u673a\u89c6\u89c9\u3001\u8bed\u97f3\u8bc6\u522b\u3001\u81ea\u7136\u8bed\u97f3\u5904\u7406\u3001\u533b\u5b66\u56fe\u50cf\u5904\u7406\u7b49\u9886\u57df\u4e2d\u3002\u4ece\u6570\u5b66\u672c\u8d28\u4e0a\u6765\u770b\uff0c\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u4e00\u4e2a\u6620\u5c04\u51fd\u6570\u800c\u5df2\uff0c\u5728\u4e0a\u4e16\u7eaa50\u5e74\u4ee3\u5c31\u6709\u4e86\u611f\u77e5\u673a\uff0c\u4f46\u4e3a\u4ec0\u4e48\u4ee5\u524d\u6ca1\u6709\u706b\u5462\uff1f \u4e3b\u8981\u6709\u4ee5\u4e0b\u7684\u4e24\u65b9\u9762\u7684\u539f\u56e0\u3002<\/p>\n<p>\u7b2c\u4e00\uff0c\u4e4b\u524d\u6ca1\u6709\u90a3\u4e48\u5927\u89c4\u6a21\u7684\u6570\u636e\u91cf\uff1b<\/p>\n<p>\u7b2c\u4e8c\uff0c\u4ee5\u524d\u7684\u5de5\u7a0b\u6280\u672f\uff08\u5148\u8fdb\u4f18\u5316\u7b97\u6cd5\u53ca\u652f\u6301\u5927\u89c4\u6a21\u5e76\u884c\u8ba1\u7b97\u7684GPU\u786c\u4ef6\uff09\u65e0\u6cd5\u6c42\u89e3\u7684\u5f88\u6df1\u7684\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5728\u4e0a\u4e2a\u4e16\u7eaa90\u5e74\u4ee3\uff0c\u5404\u79cd\u6d45\u5c42\u6a21\u578b\u5927\u884c\u5176\u9053\uff0c\u6bd4\u5982\u53ea\u6709\u4e00\u5c42\u9690\u5c42\u7684\u652f\u6491\u5411\u91cf\u673a\uff08Support Vector Machine\uff0cSVM\uff09\u4ee5\u53ca\u6ca1\u6709\u9690\u5c42\u7684\u903b\u8f91\u56de\u5f52\u65b9\u6cd5\uff08Logistic Regression\uff0cLR\uff09\u7b49\u3002<\/p>\n<p>\u76f4\u5230\u6700\u8fd1\u51e0\u5e74\uff0c\u968f\u7740\u5404\u79cd\u4f20\u611f\u5668\u7684\u5927\u91cf\u4f7f\u7528\u4ee5\u53ca\u79fb\u52a8\u4e92\u8054\u7f51\u7684\u5e7f\u6cdb\u5e94\u7528\uff0c\u80fd\u591f\u83b7\u53d6\u548c\u4ea7\u751f\u6d77\u91cf\uff08PB\u7ea7\u751a\u81f3ZB\u7ea7\uff09\u7684\u6570\u636e\uff08\u6bd4\u5982\u6587\u672c\u3001\u56fe\u50cf\u3001\u8bed\u97f3\u7b49\uff09\u3002\u7279\u522b\u662fImageNet\u56fe\u50cf\u6570\u636e\u5e93\u7684\u8bde\u751f\u4ee5\u53ca\u57fa\u4e8e\u8be5\u6570\u636e\u5e93\u7684\u5404\u79cd\u7ade\u8d5b\uff0c\u76f4\u63a5\u5c06\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\u4e2d\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u7814\u7a76\u4e0e\u5e94\u7528\u63a8\u5411\u4e86\u201c\u843d\u5730\u201d\uff0c\u50ac\u751f\u4e86\u5927\u91cf\u7684\u8ba1\u7b97\u673a\u89c6\u89c9\u7684\u4eba\u5de5\u667a\u80fd\u516c\u53f8\u3002<\/p>\n<p>8.8.      \u8fc7\u62df\u5408<\/p>\n<p>\u81ea\u4ece\u6df1\u5ea6\u5b66\u4e60\u706b\u4e86\u540e\uff0c\u5404\u79cd\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff08\u6216CNN\u7f51\u7edc\uff09\u968f\u4e4b\u4ea7\u751f\u4e86\uff0c\u6bd4\u59822012\u5e74\u7684AlexNet\u67098\u5c42\uff1b2014\u5e74\u7684VGG-19\u670919\u5c42\uff1b2014\u5e74\u7684GoogleNet\u670922\u5c42\uff1b2015\u5e74\u7684ResNet\u6709152\u5c42\uff01\u751a\u81f3\u8fd8\u51fa\u73b0\u4e86\u4e0a\u5343\u5c42\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff01<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u53ef\u77e5\uff0c\u62df\u5408\u51fd\u6570\u6240\u5e26\u7684\u53c2\u6570\u7684\u4e2a\u6570\u4e0e\u6837\u672c\u6570\u636e\u7684\u4e2a\u6570\u4e4b\u95f4\u7684\u5dee\u4ee3\u8868\u7740\u8fd9\u4e2a\u62df\u5408\u51fd\u6570\u7684\u201c\u81ea\u7531\u5ea6\u201d\u3002\u7f51\u7edc\u8d8a\u6765\u8d8a\u201c\u6df1\u201d\u540e\uff0c\u62df\u5408\u6a21\u578b\u4e2d\u7684\u53ef\u8c03\u6574\u53c2\u6570\u7684\u6570\u91cf\u5c31\u975e\u5e38\u5927\uff0c\u901a\u5e38\u80fd\u8fbe\u5230\u767e\u4e07\u8ba1\u751a\u81f3\u51e0\u5341\u4ebf\u7ea7\u3002\u56e0\u6b64\uff0c\u5c42\u6570\u5f88\u5927\u7684\u6df1\u5ea6\u7f51\u7edc\uff08\u6a21\u578b\u8fc7\u4e8e\u590d\u6742\uff09\u80fd\u591f\u8868\u8fbe\u4e00\u4e2a\u81ea\u7531\u5ea6\u975e\u5e38\u5927\u7684\u51fd\u6570\u7a7a\u95f4\uff0c\u751a\u81f3\u8fdc\u9ad8\u4e8e\u76ee\u6807\u51fd\u6570\u7a7a\u95f4\uff08\u8fc7\u5b8c\u5907\u7a7a\u95f4\uff09\uff0c\u5373\u81ea\u7531\u5ea6\u8fdc\u5927\u4e8e0\u3002\u8fd9\u6837\u5c31\u5f88\u5bb9\u6613\u5bfc\u81f4\u8fc7\u62df\u5408\uff08Overfitting\uff09\uff0c\u5982\u524d\u9762\u6240\u8ba8\u8bba\u8fc7\u7684\u56fe2\uff08\u53f3\uff09\u6240\u793a\u3002<\/p>\n<p>\u8fc7\u62df\u5408\u53ef\u4ee5\u4f7f\u5f97\u62df\u5408\u6a21\u578b\u80fd\u591f\u63d2\u503c\u6240\u6709\u6837\u672c\u6570\u636e\uff08\u62df\u5408\u8bef\u5dee\u4e3a0\uff01\uff09\u3002\u4f46\u62df\u5408\u8bef\u5dee\u4e3a0\u4e0d\u4ee3\u8868\u6a21\u578b\u5c31\u662f\u597d\u7684\uff0c\u56e0\u4e3a\u6a21\u578b\u53ea\u5728\u8bad\u7ec3\u96c6\u4e0a\u8868\u73b0\u597d\uff1b\u7531\u4e8e\u6a21\u578b\u62df\u5408\u4e86\u8bad\u7ec3\u6837\u672c\u6570\u636e\u4e2d\u7684\u566a\u58f0\uff0c\u4f7f\u5f97\u5b83\u5728\u6d4b\u8bd5\u96c6\u4e0a\u8868\u73b0\u53ef\u80fd\u4e0d\u597d\uff0c\u6cdb\u5316\u6027\u80fd\u5dee\u3002\u4e3a\u6b64\uff0c\u4eba\u4eec\u91c7\u53d6\u4e86\u4e0d\u540c\u7684\u65b9\u6cd5\u6765\u7f13\u89e3\u8fc7\u62df\u5408\uff08\u65e0\u6cd5\u5b8c\u5168\u907f\u514d\uff09\uff0c\u6bd4\u5982\u6b63\u5219\u5316\u3001\u6570\u636e\u589e\u5e7f\u3001Dropout\u3001\u7f51\u7edc\u526a\u679d\u7b49\u3002<\/p>\n<p>\u5728\u4f7f\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u6765\u505a\u6df1\u5ea6\u5b66\u4e60\u7684\u5e94\u7528\u4e2d\uff0c\u5f88\u591a\u5de5\u4f5c\u90fd\u662f\u76f4\u63a5\u4f7f\u7528\u73b0\u6709\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff0c\u6216\u8005\u6539\u9020\u73b0\u6709\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3002\u5982\u679c\u7f51\u7edc\u8bbe\u8ba1\u4e0d\u591f\u597d\uff0c\u5927\u90e8\u5206\u7ed3\u679c\u90fd\u53ef\u80fd\u6709\u8fc7\u62df\u5408\u7684\u73b0\u8c61\u3002<\/p>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u6311\u9009\u6837\u672c\u6570\u636e\u4e2d\u7684\u4e00\u90e8\u5206\u4f5c\u4e3a\u8bad\u7ec3\u6570\u636e\u96c6\uff0c\u5176\u4ed6\u7684\u4f5c\u4e3a\u6d4b\u8bd5\u6570\u636e\u96c6\u3002\u5982\u679c\u7f51\u7edc\u5728\u8bad\u7ec3\u6570\u636e\u96c6\u4e0a\u8868\u73b0\u597d\uff08\u5373\u635f\u5931\u51fd\u6570\u5f88\u5c0f\uff09\uff0c\u800c\u5728\u6d4b\u8bd5\u6570\u636e\u96c6\u4e0a\u8868\u73b0\u4e0d\u591f\u597d\uff0c\u90a3\u4e48\u5c31\u53ef\u80fd\u53d1\u751f\u4e86\u8fc7\u62df\u5408\uff0c\u6b64\u65f6\u5c31\u9002\u5f53\u51cf\u5c11\u7f51\u7edc\u7684\u5c42\u6570\u6216\u8005\u8282\u70b9\u6570\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u9700\u8981\u6709\u8010\u5fc3\uff0c\u53ef\u80fd\u9700\u8981\u82b1\u8d39\u5f88\u957f\u65f6\u95f4\u624d\u80fd\u8c03\u5230\u4e00\u4e2a\u5408\u9002\u7684\u7f51\u7edc\u3002\u9700\u8981\u9760\u611f\u89c9\u3001\u7ecf\u9a8c\u548c\u8fd0\u6c14\u3002\u56e0\u6b64\uff0c\u6709\u4eba\u620f\u79f0\u8c03\u8bd5\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u8fc7\u7a0b\u4e3a\u201c\u70bc\u4e39\u201d\u3002<\/p>\n<p>8.9.      \u7c7b\u6bd4\u795e\u7ecf\u79d1\u5b66\u7684\u89e3\u91ca<\/p>\n<p>\u6211\u4eec\u5df2\u4ece\u51fd\u6570\u903c\u8fd1\u8bba\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u4e86\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u672c\u8d28\u662f\u4f20\u7edf\u903c\u8fd1\u51fd\u6570\u7684\u4e00\u4e2a\u63a8\u5e7f\uff0c\u7531\u4eba\u5de5\u9009\u53d6\u57fa\u51fd\u6570\u5230\u81ea\u52a8\u5b66\u4e60\u57fa\u51fd\u6570\uff0c\u7531\u4eba\u5de5\u63d0\u53d6\u7279\u5f81\u5230\u81ea\u52a8\u8ba1\u7b97\u7279\u5f81\uff08\u53c2\u6570\u5316\uff09\uff0c\u80fd\u591f\u8f83\u5bb9\u6613\u7406\u89e3\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60\u662f\u5982\u4f55\u5de5\u4f5c\u7684\u3002<\/p>\n<p>\u5728\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0c\u4eba\u4eec\u4ece\u751f\u7269\u795e\u7ecf\u7f51\u7edc\u7684\u89d2\u5ea6\u6765\u89e3\u91ca\u548c\u7406\u89e3\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u5de5\u4f5c\u539f\u7406\uff0c\u5c06\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u770b\u6210\u4e3a\u4e00\u4e2a\u53ef\u4ee5\u6a21\u62df\u4eba\u8111\u5de5\u4f5c\u884c\u4e3a\u7684\u51fd\u6570\u3002<\/p>\n<p>\u5728\u751f\u7269\u795e\u7ecf\u79d1\u5b66\uff08Neuroscience\uff0c\u5305\u62ec\u8111\u79d1\u5b66\u3001\u8ba4\u77e5\u795e\u7ecf\u79d1\u5b66\u7b49\uff09\u7684\u7814\u7a76\u4e2d\uff0c\u4eba\u4eec\u53d1\u73b0\uff0c\u4eba\u4f53\u7684\u795e\u7ecf\u5143\u901a\u8fc7\u6811\u7a81\u63a5\u53d7\u4fe1\u53f7\u3002\u8fd9\u4e9b\u4fe1\u606f\u6216\u4fe1\u53f7\u968f\u540e\u88ab\u4f20\u9012\u5230\u8111\u7ec6\u80de\u6216\u7ec6\u80de\u4f53\u3002\u5728\u7ec6\u80de\u4f53\u5185\u90e8\uff0c\u6240\u6709\u7684\u4fe1\u606f\u5c06\u88ab\u52a0\u5de5\u751f\u6210\u4e00\u4e2a\u8f93\u51fa\u3002\u5f53\u8be5\u8f93\u51fa\u7ed3\u679c\u8fbe\u5230\u67d0\u4e00\u9608\u503c\u65f6\uff0c\u795e\u7ecf\u5143\u5c31\u4f1a\u5174\u594b\uff0c\u5e76\u901a\u8fc7\u8f74\u7a81\u4f20\u9012\u4fe1\u606f\uff0c\u7136\u540e\u901a\u8fc7\u7a81\u89e6\u4f20\u9012\u5230\u5176\u4ed6\u76f8\u8fde\u7684\u795e\u7ecf\u5143\u3002\u795e\u7ecf\u5143\u95f4\u4f20\u8f93\u7684\u4fe1\u53f7\u91cf\u53d6\u51b3\u4e8e\u8fde\u63a5\u7684\u5f3a\u5ea6\u3002\u5982\u56fe21\uff08\u5de6\uff09\u3002<\/p>\n<p>\u6211\u4eec\u6765\u7c7b\u6bd4\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff1a\u5982\u679c\u628a\u6811\u7a81\u60f3\u8c61\u6210\u4eba\u5de5\u667a\u80fd\u7f51\u7edc\u4e2d\u57fa\u4e8e\u7a81\u89e6\u611f\u77e5\u5668\u7684\u88ab\u8d4b\u4e88\u4e86\u6743\u91cd\u7684\u8f93\u5165\u3002\u7136\u540e\uff0c\u8be5\u8f93\u5165\u5728\u4eba\u5de5\u667a\u80fd\u7f51\u7edc\u7684\u201c\u7ec6\u80de\u4f53\u201d\uff08\u795e\u7ecf\u5143\uff09\u4e2d\u76f8\u52a0\u3002\u5982\u679c\u5f97\u51fa\u7684\u8f93\u51fa\u503c\u5927\u4e8e\u9608\u503c\u5355\u5143\uff0c\u90a3\u4e48\u795e\u7ecf\u5143\u5c31\u4f1a\u201c\u5174\u594b\u201d\uff08\u6fc0\u6d3b\uff09\uff0c\u5e76\u5c06\u8f93\u51fa\u4f20\u9012\u5230\u5176\u5b83\u795e\u7ecf\u5143\uff0c\u5982\u56fe21\uff08\u53f3\uff09\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image162.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe21. \u5de6\uff1a\u4eba\u8111\u795e\u7ecf\u5143\u7ed3\u6784\uff1b\u53f3\uff1a\u4ece\u751f\u7269\u795e\u7ecf\u7f51\u7edc\u7c7b\u6bd4\u5f97\u51fa\u7684\u4eba\u5de5\u795e\u7ecf\u5143\u7ed3\u6784\u3002<\/p>\n<p>\uff08\u56fe\u7247\u6765\u81ea\u4e92\u8054\u7f51\uff09<\/p>\n<p>\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\uff0c\u4eba\u4eec\u4e5f\u4ece\u89c6\u89c9\u795e\u7ecf\u79d1\u5b66\uff08Visual Neuroscience\uff09\u4e2d\u7c7b\u6bd4\u6765\u89e3\u91ca\u4e86\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\u7528\u5f97\u6700\u591a\u7684\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff08CNN\uff09\u7684\u5de5\u4f5c\u673a\u7406\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image163.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe22. \u89c6\u89c9\u76ae\u5c42\u7ed3\u6784\u3002\uff08\u56fe\u7247\u6765\u81ea\u4e92\u8054\u7f51\uff09<\/p>\n<p>\u7531\u89c6\u89c9\u673a\u7406\u7684\u7814\u7a76\u53d1\u73b0\uff0c\u52a8\u7269\u5927\u8111\u7684\u89c6\u89c9\u76ae\u5c42\u5177\u6709\u5206\u5c42\u7ed3\u6784\u3002\u773c\u775b\u5c06\u770b\u5230\u7684\u666f\u8c61\u6210\u50cf\u5728\u89c6\u7f51\u819c\u4e0a\uff0c\u89c6\u7f51\u819c\u628a\u5149\u5b66\u4fe1\u53f7\u8f6c\u6362\u6210\u7535\u4fe1\u53f7\uff0c\u4f20\u9012\u5230\u5927\u8111\u7684\u89c6\u89c9\u76ae\u5c42\uff08Visual cortex\uff09\uff0c\u89c6\u89c9\u76ae\u5c42\u662f\u5927\u8111\u4e2d\u8d1f\u8d23\u5904\u7406\u89c6\u89c9\u4fe1\u53f7\u7684\u90e8\u5206\u30021959\u5e74\uff0c\u6709\u79d1\u5b66\u5bb6\u8fdb\u884c\u4e86\u4e00\u6b21\u5b9e\u9a8c\uff0c\u4ed6\u4eec\u5728\u732b\u7684\u5927\u8111\u521d\u7ea7\u89c6\u89c9\u76ae\u5c42\u5185\u63d2\u5165\u7535\u6781\uff0c\u5728\u732b\u7684\u773c\u524d\u5c55\u793a\u5404\u79cd\u5f62\u72b6\u3001\u7a7a\u95f4\u4f4d\u7f6e\u3001\u89d2\u5ea6\u7684\u5149\u5e26\uff0c\u7136\u540e\u6d4b\u91cf\u732b\u5927\u8111\u795e\u7ecf\u5143\u653e\u51fa\u7684\u7535\u4fe1\u53f7\u3002\u5b9e\u9a8c\u53d1\u73b0\uff0c\u5f53\u5149\u5e26\u5904\u4e8e\u67d0\u4e00\u4f4d\u7f6e\u548c\u89d2\u5ea6\u65f6\uff0c\u7535\u4fe1\u53f7\u6700\u4e3a\u5f3a\u70c8\uff1b\u4e0d\u540c\u7684\u795e\u7ecf\u5143\u5bf9\u5404\u79cd\u7a7a\u95f4\u4f4d\u7f6e\u548c\u65b9\u5411\u504f\u597d\u4e0d\u540c\u3002\u8fd9\u4e00\u6210\u679c\u540e\u6765\u8ba9\u4ed6\u4eec\u83b7\u5f97\u4e86\u8bfa\u8d1d\u5c14\u5956\u3002<\/p>\n<p>\u76ee\u524d\u5df2\u7ecf\u8bc1\u660e\uff0c\u89c6\u89c9\u76ae\u5c42\u5177\u6709\u5c42\u6b21\u7ed3\u6784\u3002\u4ece\u89c6\u7f51\u819c\u4f20\u6765\u7684\u4fe1\u53f7\u9996\u5148\u5230\u8fbe\u521d\u7ea7\u89c6\u89c9\u76ae\u5c42\uff08primary visual cortex\uff09\uff0c\u5373V1\u76ae\u5c42\u3002V1\u76ae\u5c42\u7b80\u5355\u795e\u7ecf\u5143\u5bf9\u4e00\u4e9b\u7ec6\u8282\u3001\u7279\u5b9a\u65b9\u5411\u7684\u56fe\u50cf\u4fe1\u53f7\u654f\u611f\u3002V1\u76ae\u5c42\u5904\u7406\u4e4b\u540e\uff0c\u5c06\u4fe1\u53f7\u4f20\u5bfc\u5230V2\u76ae\u5c42\u3002V2\u76ae\u5c42\u5c06\u8fb9\u7f18\u548c\u8f6e\u5ed3\u4fe1\u606f\u8868\u793a\u6210\u7b80\u5355\u5f62\u72b6\uff0c\u7136\u540e\u7531V4\u76ae\u5c42\u4e2d\u7684\u795e\u7ecf\u5143\u8fdb\u884c\u5904\u7406\uff0c\u5b83\u989c\u8272\u4fe1\u606f\u654f\u611f\u3002\u590d\u6742\u7269\u4f53\u6700\u7ec8\u5728IT\u76ae\u5c42\uff08inferior temporal cortex\uff09\u88ab\u8868\u793a\u51fa\u6765\u3002<\/p>\n<p>\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u770b\u6210\u662f\u4e0a\u9762\u8fd9\u79cd\u673a\u5236\u7684\u7b80\u5355\u6a21\u4eff\u3002\u5b83\u7531\u591a\u4e2a\u5377\u79ef\u5c42\u6784\u6210\uff0c\u6bcf\u4e2a\u5377\u79ef\u5c42\u5305\u542b\u591a\u4e2a\u5377\u79ef\u6838\uff0c\u7528\u8fd9\u4e9b\u5377\u79ef\u6838\u4ece\u5de6\u5411\u53f3\u3001\u4ece\u4e0a\u5f80\u4e0b\u4f9d\u6b21\u626b\u63cf\u6574\u4e2a\u56fe\u50cf\uff0c\u5f97\u5230\u79f0\u4e3a\u7279\u5f81\u56fe\uff08feature map\uff09\u7684\u8f93\u51fa\u6570\u636e\u3002\u7f51\u7edc\u524d\u9762\u7684\u5377\u79ef\u5c42\u6355\u6349\u56fe\u50cf\u5c40\u90e8\u3001\u7ec6\u8282\u4fe1\u606f\uff0c\u6709\u5c0f\u7684\u611f\u53d7\u91ce\uff0c\u5373\u8f93\u51fa\u56fe\u50cf\u7684\u6bcf\u4e2a\u50cf\u7d20\u53ea\u5229\u7528\u8f93\u5165\u56fe\u50cf\u5f88\u5c0f\u7684\u4e00\u4e2a\u8303\u56f4\u3002\u540e\u9762\u7684\u5377\u79ef\u5c42\u611f\u53d7\u91ce\u9010\u5c42\u52a0\u5927\uff0c\u7528\u4e8e\u6355\u83b7\u56fe\u50cf\u66f4\u590d\u6742\uff0c\u66f4\u62bd\u8c61\u7684\u4fe1\u606f\u3002\u7ecf\u8fc7\u591a\u4e2a\u5377\u79ef\u5c42\u7684\u8fd0\u7b97\uff0c\u6700\u540e\u5f97\u5230\u56fe\u50cf\u5728\u5404\u4e2a\u4e0d\u540c\u5c3a\u5ea6\u7684\u62bd\u8c61\u8868\u793a\uff08\u7531\u5e95\u5c42\u5230\u9ad8\u5c42\u7684\u7279\u5f81\u8868\u8fbe\uff09\uff0c\u5982\u56fe23\u6240\u793a\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image164.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe23. \u57fa\u4e8e\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u6240\u5f97\u5230\u7684\u4eba\u8138\u56fe\u50cf\u7684\u5206\u5c42\u7279\u5f81\u3002<\/p>\n<p>\uff08\u56fe\u7247\u6765\u81ea\u4e8eStanford\u5927\u5b66\u7684\u8bba\u6587\uff09<\/p>\n<p>\u7b14\u8005\u8ba4\u4e3a\uff0c\u5229\u7528\u795e\u7ecf\u79d1\u5b66\u7684\u795e\u7ecf\u5143\u6216\u795e\u7ecf\u7f51\u7edc\u6765\u89e3\u91ca\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff0c\u8fd9\u4ec5\u4ec5\u662f\u7c7b\u6bd4\u800c\u5df2\u3002\u4ece\u6211\u4eec\u7684\u5206\u6790\u53ef\u77e5\uff0c\u6df1\u5ea6\u5b66\u4e60\u4e2d\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u5e76\u6ca1\u6709\u771f\u6b63\u7684\u8ba4\u77e5\u548c\u5b66\u4e60\uff01\u5982\u679c\u6211\u4eec\u4eba\u7c7b\u5bf9\u81ea\u5df1\u7684\u8ba4\u77e5\u7cfb\u7edf\u65e0\u6cd5\u5b8c\u5168\u4e86\u89e3\u7684\u8bdd\uff0c\u6211\u4eec\u662f\u5f88\u96be\u53d1\u5c55\u51fa\u771f\u6b63\u7684\u4eba\u5de5\u667a\u80fd\u6280\u672f\u3002<\/p>\n<p>8.10.    \u6df1\u5ea6\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u5c40\u9650\uff1a\u4fdd\u6301\u7ed3\u6784\u7684\u6620\u5c04<\/p>\n<p>\u6211\u4eec\u4ece\u6570\u5b66\u4e0a\u7406\u89e3\u4e86\u6df1\u5ea6\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u672c\u8d28\u4e0a\u662f\u8868\u8fbe\u4e0d\u540c\u7ef4\u6570\u7a7a\u95f4\u4e4b\u95f4\u7684\u4e00\u4e2a\u6620\u5c04\uff08\u51fd\u6570\uff09\u3002\u7ed9\u4e86\u4e00\u4e9b\u6837\u672c\u70b9\u540e\uff0c\u901a\u8fc7\u8c03\u6574\u7f51\u7edc\u7684\u53c2\u6570\u6743\u7cfb\u6570\uff0c\u4e0d\u65ad\u6781\u5c0f\u5316\u635f\u5931\u51fd\u6570\uff0c\u4ece\u800c\u8fbe\u5230\u6700\u597d\u7684\u62df\u5408\u7ed3\u679c\u5f97\u5230\u4e86\u62df\u5408\u51fd\u6570\u3002<\/p>\n<p>\u8fd9\u4e2a\u62df\u5408\u8fc7\u7a0b\u53ea\u6781\u5c0f\u5316\u4e86\u9010\u70b9\u7684\u8bef\u5dee\u6216\u8005\u7d2f\u79ef\u9010\u70b9\u8bef\u5dee\uff0c\u800c\u65e0\u6cd5\u8003\u8651\u70b9\u4e0e\u5468\u56f4\u70b9\u4e4b\u95f4\u7684\u5176\u4ed6\u4fe1\u606f\uff08\u6bd4\u5982\u90bb\u57df\u51e0\u4f55\u7ed3\u6784\u3001\u5c40\u90e8\u51e0\u4f55\u5ea6\u91cf\u3001\u6d41\u5f62\u7684\u6574\u4f53\u62d3\u6251\u7ed3\u6784\u7b49\uff09\u3002\u5982\u679c\u8981\u8003\u8651\u70b9\u4e4b\u95f4\u7684\u51e0\u4f55\u4e0e\u62d3\u6251\u7684\u7ed3\u6784\u4fe1\u606f\uff0c\u5219\u6df1\u5ea6\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u5c31\u65e0\u80fd\u4e3a\u529b\uff08\u5f53\u7136\u4e00\u5b9a\u8981\u6539\u9020\u4e5f\u662f\u53ef\u4ee5\u7684\uff09\uff0c\u8fd9\u65f6\u5c31\u9700\u8981\u5176\u4ed6\u7684\u6570\u5b66\u65b9\u6cd5\u4e86\u3002\u6709\u70b9\u50cf\u6570\u5b66\u5206\u6790\u4e2d\uff0c\u9010\u70b9\u6536\u655b\u548c\u4e00\u81f4\u6536\u655b\uff0c\u9010\u70b9\u8fde\u7eed\u548c\u4e00\u81f4\u8fde\u7eed\u7684\u533a\u522b\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u524d\u9762\u4ecb\u7ecd\u7684\u6d41\u5f62\u5b66\u4e60\u4e2d\uff0cLLE\u65b9\u6cd5\u4fdd\u6301\u6bcf\u4e2a\u6837\u672c\u70b9\u4e0e\u5b83\u76f8\u90bb\u7684\u591a\u4e2a\u70b9\u7684\u7ebf\u6027\u7ec4\u5408\uff08\u4f53\u73b0\u4e86\u5c40\u90e8\u7ebf\u6027\uff09\u6765\u91cd\u6784\u4f4e\u7ef4\u7a7a\u95f4\u7684\u70b9\u7684\u5206\u5e03\uff0c\u76f8\u5f53\u4e8e\u7528\u5206\u6bb5\u7684\u7ebf\u6027\u9762\u7247\u8fd1\u4f3c\u4ee3\u66ff\u590d\u6742\u7684\u51e0\u4f55\u5f62\u72b6\uff0c\u6837\u672c\u6295\u5f71\u5230\u4f4e\u7ef4\u7a7a\u95f4\u4fdd\u6301\u8fd9\u79cd\u7ebf\u6027\u91cd\u6784\u5173\u7cfb\uff0c\u5982\u56fe24\uff08\u5de6\uff09\u6240\u793a\u3002Isomap\u65b9\u6cd5\u5e0c\u671b\u4fdd\u6301\u6570\u636e\u5728\u4f4e\u7ef4\u7a7a\u95f4\u7684\u6620\u5c04\u4e4b\u540e\u80fd\u591f\u4fdd\u6301\u6d41\u5f62\u4e0a\u7684\u6d4b\u5730\u7ebf\u8ddd\u79bb\uff0c\u5373\u5168\u5c40\u7684\u51e0\u4f55\u7ed3\u6784\uff0c\u5982\u56fe24\uff08\u53f3\uff09\u6240\u793a\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image165.jpg\" alt=\"img\" \/>  <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image166.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe24. \u6d41\u5f62\u5b66\u4e60\u3002\u5de6\uff1a\u4fdd\u6301\u5c40\u90e8\u7684\u51e0\u4f55\u4fe1\u606f\uff08LLE\uff09\uff1b\u53f3\uff1a\u4fdd\u6301\u5168\u5c40\u7684\u8ddd\u79bb\u4fe1\u606f\uff08Isomap\uff09\u3002<\/p>\n<p>\uff08\u56fe\u7247\u5206\u522b\u6765\u81ea\u4e8e\u8bba\u6587[8-4]\u548c[8-5]\uff09<\/p>\n<p>\u518d\u5982\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u548c\u51e0\u4f55\u5904\u7406\u9886\u57df\uff0c\u6211\u4eec\u505a\u7684\u5f88\u591a\u6620\u5c04\uff08\u6bd4\u5982\u4e09\u7ef4\u7f51\u683c\u66f2\u9762\u7684\u53c2\u6570\u5316\uff09\uff0c\u4e5f\u9700\u8981\u4fdd\u6301\u66f2\u9762\u4e0a\u7684\u67d0\u4e9b\u51e0\u4f55\u6027\u8d28\uff08\u4fdd\u89d2\u5ea6\u3001\u4fdd\u9762\u79ef\u3001\u4fdd\u5f62\u7b49\uff09\uff0c\u4e5f\u53d1\u5c55\u51fa\u8bb8\u591a\u4e0d\u540c\u7684\u6c42\u89e3\u6620\u5c04\u7684\u65b9\u6cd5\u548c\u6280\u5de7\u3002\u4f8b\u5982\uff0c\u4ee5\u4e0b\u4e24\u4e2a\u5de5\u4f5c\u662f\u6211\u4eec\u505a\u7684\u6709\u5173\u4e09\u7ef4\u66f2\u9762\u53c2\u6570\u5316\u5230\u4e8c\u7ef4\u5e73\u9762\u7684\u5de5\u4f5c\uff0c\u7b2c\u4e00\u4e2a\u5de5\u4f5c\u662f\u66f2\u9762\u53c2\u6570\u5316\u5de5\u4f5c\u7684\u7ecf\u5178\u65b9\u6cd5\u4e4b\u4e00\uff0c\u5df2\u7ecf\u88ab\u96c6\u6210\u52303D System\u516c\u53f8\u7684\u5efa\u6a21\u8f6f\u4ef6\u4ee5\u53ca\u8457\u540d\u7684\u8ba1\u7b97\u51e0\u4f55\u7b97\u6cd5<a href=\"https:\/\/www.cgal.org\/\">CGAL\u5e93<\/a>\uff08The Computational Geometry Algorithms Library\uff09\u4e2d\u3002\u7b2c\u4e8c\u4e2a\u5de5\u4f5c\u662f\u4eca\u5e74\u6211\u4eec\u6700\u65b0\u7684\u4e00\u4e2a\u5de5\u4f5c\uff0c\u80fd\u5feb\u901f\u751f\u6210\u65e0\u7ffb\u8f6c\u548c\u4f4e\u626d\u66f2\u7684\u7f51\u683c\u53c2\u6570\u5316\uff0c\u8bba\u6587\u5373\u5c06\u5728\u4e0b\u5468\u7684Siggraph 2018\u4f1a\u8bae\u4e0a\u6c47\u62a5\u3002<\/p>\n<p>[8-7] Ligang Liu, Lei Zhang, Yin Xu, Craig Gotsman, Steven J. Gortler. A Local\/Global Approach to Mesh Parameterization. Computer Graphics Forum (Proc. Eurographics Symposium on Geometry Processing (SGP)), 27(5), 1495-1504, 2008.<\/p>\n<p>[8-8] Ligang Liu, Chunyang Ye, Ruiqi Ni, Xiao-Ming Fu. Progressive Parameterizations. ACM Transactions on Graphics (Proc. Siggraph), 37(4), Article 41: 1-12, 2018.<\/p>\n<p>\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0c\u6709\u65f6\u6211\u4eec\u4e5f\u9700\u8981\u5c06\u4e09\u7ef4\u7a7a\u95f4\u7684\u4e8c\u7ef4\u6d41\u5f62\u66f2\u9762\u6620\u5c04\u5230\u53e6\u4e00\u4e2a\u89c4\u5219\u4e8c\u7ef4\u6d41\u5f62\u66f2\u9762\uff0c\u6bd4\u5982\u7403\u9762\u4e0a\uff0c\u8fd9\u65f6\u79f0\u4e3a\u7403\u9762\u53c2\u6570\u5316\u3002\u5982\u8bfb\u8005\u6709\u5174\u8da3\u53ef\u9605\u8bfb\u6211\u4eec\u5982\u4e0b\u76843\u7bc7\u6709\u5173\u7403\u9762\u53c2\u6570\u5316\u7684\u5de5\u4f5c\u3002<\/p>\n<p>[8-9] Xin Hu, Xiao-Ming Fu, Ligang Liu. Advanced Hierarchical Spherical Parameterizations. IEEE Transactions on Visualization and Computer Graphics, to appear, 2018.<\/p>\n<p>[8-10] Chunxue Wang, Xin Hu, Xiaoming Fu, Ligang Liu. Bijective Spherical Parametrization with Low Distortion. Computers&amp;Graphics (Proc. SMI), 58: 161-171, 2016.<\/p>\n<p>[8-11] Chunxue Wang, Zheng Liu, Ligang Liu. As-Rigid-As-Possible Spherical Parameterization. Graphical Models (Proc. GMP), 76(5): 457-467, 2014.<\/p>\n<p>\u53e6\u5916\uff0c\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u53ca\u8ba1\u7b97\u673a\u8f85\u52a9\u51e0\u4f55\u8bbe\u8ba1\u9886\u57df\uff0c\u6211\u4eec\u8fd8\u6709\u72ec\u7279\u7684\u66f2\u7ebf\u548c\u51fd\u6570\u7684\u6784\u9020\u65b9\u6cd5\uff0c\u5982\u901a\u8fc7Bernstein\u57fa\u51fd\u6570\u6784\u9020\u7684Bezier\u66f2\u7ebf\u66f2\u9762\uff0c\u901a\u8fc7B\u6837\u6761\u57fa\u6784\u9020\u7684B\u6837\u6761\u66f2\u7ebf\u66f2\u9762\uff08\u5206\u6bb5Bezier\u66f2\u7ebf\u66f2\u9762\uff09\uff0c\u4ee5\u53ca\u66f4\u4e00\u822c\u7684\u975e\u5747\u6709\u6709\u7406B\u6837\u6761\u66f2\u7ebf\u66f2\u9762\uff0c\u901a\u8fc7\u63a7\u5236\u9876\u70b9\u5c31\u80fd\u5f88\u76f4\u89c2\u63a7\u5236\u66f2\u7ebf\u66f2\u9762\u7684\u5f62\u72b6\uff0c\u800c\u4e14\u53d1\u5c55\u51fa\u975e\u5e38\u5b8c\u5907\u7684\u7406\u8bba\u53ca\u8bbe\u8ba1\u65b9\u6cd5\uff0c\u5982\u56fe25\u6240\u793a\u3002\u8fd9\u4e9b\u72ec\u7279\u7684\u66f2\u7ebf\u66f2\u9762\u7684\u6784\u9020\u65b9\u6cd5\u4e5f\u662f\u6211\u4eec\u9886\u57df\u72ec\u7279\u7684\uff0c\u5df2\u6210\u4e3a\u73b0\u4ee3\u5de5\u4e1a\u4e2d\u4ea7\u54c1\u66f2\u9762\u9020\u578b\u7684\u5de5\u4e1a\u6807\u51c6\uff08\u6807\u51c6\u6570\u5b66\u8868\u8fbe\uff09\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image167.jpg\" alt=\"img\" \/> <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image168.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe25. NURBS\u66f2\u7ebf\u66f2\u9762\uff1a\u4ea7\u54c1\u66f2\u9762\u9020\u578b\u7684\u5de5\u4e1a\u6807\u51c6\u3002\uff08\u56fe\u7247\u6765\u6e90\u4e0e\u4e92\u8054\u7f51\uff09<\/p>\n<h2><strong>\u4e5d\u3001<\/strong>  <strong>\u5b9e\u6218\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60<\/strong><\/h2>\n<p>\u7531\u4e8e\u672c\u6587\u662f\u9762\u5411\u975e\u673a\u5668\u5b66\u4e60\u4e13\u4e1a\u4ecb\u7ecd\u6df1\u5ea6\u5b66\u4e60\u7684\uff0c\u56e0\u6b64\uff0c\u7b14\u8005\u5728\u8fd9\u91cc\u53ea\u662f\u5927\u81f4\u4ecb\u7ecd\u4e00\u4e0b\u5404\u79cd\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\u65b9\u6cd5\u7684\u5b9e\u9645\u6280\u5de7\uff0c\u4e0d\u8be6\u7ec6\u5c55\u5f00\u8ba8\u8bba\uff0c\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u67e5\u9605\u66f4\u4e13\u4e1a\u7684\u4e66\u7c4d\u6216\u8bba\u6587\u3002<\/p>\n<p>9.1.      \u770b\u61c2\u5404\u79cd\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u6765\u770b\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4ec5\u4ec5\u662f\u4e00\u79cd\u51fd\u6570\u7684\u8868\u8fbe\u5f62\u5f0f\uff0c\u662f\u590d\u6742\u7684\u591a\u5c42\u590d\u5408\u51fd\u6570\u3002\u7531\u4e8e\u5b83\u6709\u5927\u91cf\u7684\u53ef\u8c03\u53c2\u6570\uff0c\u800c\u4e14\u8fd1\u5e74\u6765\u968f\u7740\u5927\u6570\u636e\u3001\u4f18\u5316\u7b97\u6cd5\u548c\u5e76\u884c\u8ba1\u7b97GPU\u786c\u4ef6\u7684\u53d1\u5c55\uff0c\u4f7f\u5f97\u7528\u5927\u89c4\u6a21\u7684\u795e\u7ecf\u7f51\u7edc\u6765\u903c\u8fd1\u548c\u62df\u5408\u5927\u6570\u636e\u6210\u4e3a\u53ef\u80fd\u3002\u81f3\u4eca\uff0c\u4e0d\u540c\u9886\u57df\u7684\u7814\u7a76\u5de5\u4f5c\u8005\u53ca\u4ea7\u4e1a\u754c\u5de5\u4f5c\u8005\u5df2\u5c06\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5e94\u7528\u5230\u5404\u884c\u5404\u4e1a\u7684\u5404\u4e2a\u95ee\u9898\uff0c\u800c\u4e14\u63d0\u51fa\u4e86\u5404\u79cd\u5f62\u5f0f\u3001\u5404\u79cd\u7ed3\u6784\u7684\u6df1\u5ea6\u7f51\u7edc\u7ed3\u6784\uff0c\u4f7f\u4eba\u773c\u82b1\u7f2d\u4e71\uff0c\u4f3c\u4e4e\u96be\u4ee5\u6349\u6478\u3002\u4f46\u4e8b\u5b9e\u5e76\u975e\u5982\u6b64\uff01<\/p>\n<p>\u4e07\u53d8\u4e0d\u79bb\u5176\u5b97\uff0c\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u4e00\u4e2a\u591a\u5c42\u590d\u5408\u51fd\u6570\u3002\u7f51\u7edc\u7ed3\u6784\u53d1\u751f\u6539\u53d8\uff0c\u5c31\u662f\u8bf4\u51fd\u6570\u7684\u590d\u5408\u5f62\u5f0f\u53d1\u751f\u4e86\u53d8\u5316\u3002\u56e0\u6b64\uff0c\u53ea\u8981\u638c\u63e1\u4e86\u8fd9\u6761\u539f\u5219\uff0c\u5404\u79cd\u590d\u6742\u7684\u795e\u7ecf\u7f51\u7edc\u4f60\u5c31\u80fd\u8f7b\u677e\u770b\u61c2\u3002\u4ea6\u53ef\u53c2\u8003\u4e92\u8054\u7f51\u4e0a\u7684\u201c<a href=\"https:\/\/blog.csdn.net\/qq_35082030\/article\/details\/73368962\">\u4e00\u6587\u770b\u61c225\u4e2a\u795e\u7ecf\u7f51\u7edc\u6a21\u578b<\/a>\u201d\u4e00\u6587\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image169.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe26. \u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\uff1a\u53ef\u4ee5\u770b\u6210\u524d\u9762\u7684\u82e5\u5e72\u5c42\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\uff08\u84dd\u8272\uff09\u4e0e\u540e\u9762\u82e5\u5e72\u5c42\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\uff08\u7ea2\u8272\uff09\u7684\u590d\u5408\u3002<\/p>\n<p>\u7b80\u5355\u5730\u8bf4\uff0c\u770b\u61c2\u5404\u79cd\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u53ea\u9700\u770b\u61c2\u5982\u4e0b3\u4e2a\u8981\u7d20\uff08\u5177\u4f53\u89e3\u91ca\u5c31\u4e0d\u8be6\u7ec6\u5c55\u5f00\u4e86\uff09\uff1a<\/p>\n<p>(1)  \u795e\u7ecf\u5143\u4e0e\u6fc0\u6d3b\u51fd\u6570\uff1a\u795e\u7ecf\u5143\u63a5\u6536\u4ec0\u4e48\u6570\u636e\uff0c\u901a\u8fc7\u4ec0\u4e48\u6837\u7684\u6fc0\u6d3b\u51fd\u6570\u8f93\u51fa\u6570\u636e\u3002\u4eba\u4eec\u53d1\u660e\u4e86\u8bb8\u591a\u4e0d\u540c\u79cd\u7c7b\u7684\u795e\u7ecf\u5143\uff0c\u6bd4\u5982\uff0c\u6c60\u5316\u795e\u7ecf\u5143\u548c\u63d2\u503c\u795e\u7ecf\u5143\uff08Pooling and interpolating cells\uff09\u3001\u6982\u7387\u795e\u7ecf\u5143\uff08Mean and standard deviation cells\uff09\u3001\u5faa\u73af\u795e\u7ecf\u5143\uff08Recurrent cells \uff09\u3001\u957f\u77ed\u671f\u8bb0\u5fc6\u795e\u7ecf\u5143\uff08Long short term memory cells\uff09\u3001\u95e8\u63a7\u5faa\u73af\u795e\u7ecf\u5143\uff08Gated recurrent cells\uff09\u7b49\u3002\u4e0d\u7ba1\u4ec0\u4e48\u6837\u5f62\u5f0f\u548c\u540d\u79f0\u7684\u795e\u7ecf\u5143\uff0c\u6211\u4eec\u53ea\u8981\u641e\u660e\u767d\u795e\u7ecf\u5143\u662f\u901a\u8fc7\u4ec0\u4e48\u6837\u7684\u51fd\u6570\u6765\u5c06\u63a5\u6536\u6570\u636e\u53d8\u4e3a\u8f93\u51fa\u6570\u636e\uff0c\u4e0d\u540c\u4e4b\u5904\u5c31\u5728\u63a5\u6536\u6570\u636e\u548c\u6fc0\u6d3b\u51fd\u6570\u4e0d\u540c\u800c\u5df2\uff0c\u5982\u56fe21\uff08\u53f3\uff09\u6240\u793a\u3002<\/p>\n<p>(2)  \u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\uff1a\u4e0d\u540c\u7684\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u4e0d\u540c\u7684\u591a\u5c42\u590d\u5408\u5f62\u5f0f\u7684\u51fd\u6570\u3002\u6bd4\u5982\uff0c\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff08Convolutional Neural Network\uff0cCNN\uff09\u5c31\u662f\u4e00\u79cd\u9650\u4e8e\u5c40\u90e8\u611f\u53d7\u91ce\u6765\u6539\u9020\u7684\u795e\u7ecf\u7f51\u7edc\uff08\u7ebf\u6027\u7ec4\u5408\u7279\u6b8a\u5316\u4e3a\u5c40\u90e8\u533a\u57df\u7684\u5377\u79ef\u64cd\u4f5c\uff0c\u4e14\u589e\u52a0\u4e86\u6c60\u5316(Pooling)\u5c42\uff09\uff0c\u7279\u522b\u9002\u5408\u4e8e\u6587\u672c\u3001\u56fe\u50cf\u53ca\u89c6\u9891\u7c7b\u6570\u636e\u7684\u6df1\u5ea6\u5b66\u4e60\u3002\u518d\u6bd4\u5982\uff0c\u6b8b\u5dee\u795e\u7ecf\u7f51\u7edc\uff08Residual Neural Network\uff0cResNet\uff09\u6709\u4e00\u79cd\u7279\u6b8a\u7684\u8fde\u63a5\uff0c\u53ef\u4ee5\u628a\u6570\u636e\u4ece\u67d0\u4e00\u9690\u5c42\u4f20\u81f3\u540e\u9762\u51e0\u5c42\uff08\u901a\u5e38\u662f2\u52305\u5c42\uff09\u3002\u8be5\u7f51\u7edc\u7684\u76ee\u7684\u4e0d\u662f\u8981\u627e\u8f93\u5165\u6570\u636e\u4e0e\u8f93\u51fa\u6570\u636e\u4e4b\u95f4\u7684\u6620\u5c04\uff0c\u800c\u662f\u81f4\u529b\u4e8e\u6784\u5efa\u8f93\u5165\u6570\u636e\u4e0e\u8f93\u51fa\u6570\u636e+\u8f93\u5165\u6570\u636e\u4e4b\u95f4\u7684\u6620\u5c04\u51fd\u6570\u3002\u672c\u8d28\u4e0a\uff0cResNet \u662f\u5728\u5b66\u4e60\u6620\u5c04\u51fd\u6570\u7684\u4e00\u9636\u5dee\u5206\uff08\u4e00\u9636\u5bfc\u6570\uff09\uff0c\u80fd\u591f\u6709\u6548\u6291\u5236\u4f18\u5316\u8fc7\u7a0b\u4e2d\u7684\u68af\u5ea6\u6d88\u5931\u3002\u7c7b\u4f3c\u5730\uff0c DenseNet (CVPR 2017) \u5b9e\u8d28\u4e0a\u662f\u5728\u5b66\u4e60\u6620\u5c04\u51fd\u6570\u7684\u9ad8\u9636\u5dee\u5206\uff0c\u56e0\u6b64\u4e5f\u80fd\u6709\u6548\u6291\u5236\u68af\u5ea6\u6d88\u5931\u73b0\u8c61\u3002\u540c\u6837\u5730\uff0c\u5176\u4ed6\u7684\u5404\u79cd\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u4e5f\u5f88\u5bb9\u6613\u770b\u61c2\u7684\uff0c\u6bd4\u5982 AutoEncoder\uff0cGAN\uff0cVariational GAN\u7b49\u3002<\/p>\n<p>(3)  \u795e\u7ecf\u7f51\u7edc\u7684\u7ec4\u5408\uff1a\u4e00\u4e2a\u591a\u5c42\u7684\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u4e00\u4e2a\u591a\u6b21\u590d\u5408\u7684\u51fd\u6570\u3002\u4e2d\u95f4\u7684\u4efb\u4f55\u4e00\u5c42\u7684\u8f93\u51fa\u90fd\u53ef\u4ee5\u770b\u6210\u4e3a\u539f\u59cb\u8f93\u5165\u6570\u636e\u7684\u4e00\u4e2a\u7279\u5f81\u3002\u5982\u56fe26\u6240\u793a\uff0c\u4e00\u4e2a\u591a\u5c42\u795e\u7ecf\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\uff1a\u53ef\u4ee5\u770b\u6210\u524d\u9762\u7684\u82e5\u5e72\u5c42\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\uff08\u84dd\u8272\uff09\u4e0e\u540e\u9762\u82e5\u5e72\u5c42\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\uff08\u7ea2\u8272\uff09\u7684\u590d\u5408\u3002\u56e0\u6b64\uff0c\u5728\u4efb\u4f55\u7684\u4e00\u4e2a\u4e2d\u95f4\u5c42\uff0c\u53ef\u4ee5\u4fee\u6539\u8f93\u51fa\u7684\u7279\u5f81\u5411\u91cf\u3001\u53ef\u4ee5\u63d2\u5165\u4e00\u4e2a\u5176\u4ed6\u7684\u795e\u7ecf\u7f51\u7edc\uff08\u5c06\u8be5\u7279\u5f81\u5411\u91cf\u4f5c\u4e3a\u8f93\u5165\uff0c\u6216\u4e0e\u5176\u4ed6\u7f51\u7edc\u7684\u7279\u5f81\u5411\u91cf\u8fdb\u884c\u53e0\u52a0\u3001\u8fd0\u7b97\u7b49\uff09\u7b49\u7b49\u3002\u5982\u679c\u5c06\u795e\u7ecf\u7f51\u7edc\u770b\u6210\u4e3a\u79ef\u6728\uff0c\u6574\u4e2a\u7ec4\u5408\u8fc7\u7a0b\u5c31\u50cf\u5728\u201c\u642d\u79ef\u6728\u201d\u3002\u8fd9\u6837\u5c31\u53ef\u4ee5\u53d1\u660e\u548c\u4ea7\u751f\u65e0\u7a77\u65e0\u5c3d\u7684\u7f51\u7edc\u7ed3\u6784\uff08\u6bd4\u5982\uff0c\u5e76\u884c\u7f51\u7edc\u3001\u7d2f\u52a0\u7f51\u7edc\u7b49\u7b49\u5f88\u591a\u7f51\u7edc\u540d\u79f0\uff09\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9700\u8981\u6839\u636e\u95ee\u9898\u672c\u8eab\u7684\u7279\u70b9\u6765\u5408\u7406\u8bbe\u8ba1\u7f51\u7edc\u7684\u7ed3\u6784\u3002\u5177\u4f53\u54ea\u79cd\u7f51\u7edc\u7ed3\u6784\u5408\u7406\uff0c\u6709\u65e0\u6700\u597d\uff0c\u90fd\u662f\u7ec4\u8981\u6839\u636e\u95ee\u9898\u672c\u8eab\u601d\u8003\u548c\u8bd5\u9a8c\u7684\uff0c\u4e3b\u8981\u662f\u8981\u770b\u635f\u5931\u51fd\u6570\u7684\u8bef\u5dee\u4ee5\u53ca\u5728\u5e94\u7528\u4e2d\u7684\u6548\u679c\u6765\u51b3\u5b9a\u7684\u3002\u8fd9\u4e2a\u6211\u4eec\u5728\u540e\u9762\u8fd8\u4f1a\u8fdb\u4e00\u6b65\u8ba8\u8bba\u3002<\/p>\n<p>9.2.      \u5982\u4f55\u8c03\u8bd5\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff1f<\/p>\n<p>\u4e00\u4e2a\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u6240\u8868\u8fbe\u7684\u51fd\u6570\u5177\u6709\u6210\u5343\u4e0a\u4e07\u4e2a\u53c2\u6570\uff0c\u4e3a\u4e86\u8ba9\u635f\u5931\u51fd\u6570\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u8fbe\u5230\u6700\u5c0f\uff0c\u5c31\u9700\u8981\u8bbe\u8ba1\u5408\u7406\u7684\u7f51\u7edc\u6765\u62df\u5408\u8fd9\u4e9b\u6570\u636e\u3002\u5728\u4f18\u5316\u7684\u8fc7\u7a0b\u4e2d\uff0c\u8981\u4fdd\u8bc1\u8fed\u4ee3\u6536\u655b\u4e5f\u662f\u5fc5\u8981\u7684\u3002<\/p>\n<p>\u4e00\u822c\u5730\uff0c\u8c03\u8bd5\u8f83\u5927\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u6240\u82b1\u8d39\u7684\u65f6\u95f4\u548c\u52b3\u529b\u6bd4\u8c03\u8bd5\u4f20\u7edf\u7a0b\u5e8f\u8981\u591a\uff0c\u800c\u4e14\u8981\u6709\u8010\u5fc3\uff01\u56e0\u4e3a\u5982\u679c\u6700\u540e\u7684\u7ed3\u679c\u4e0d\u597d\uff08\u635f\u5931\u51fd\u6570\u5f88\u5927\u6216\u8005\u4e0d\u6536\u655b\uff09\uff0c\u5982\u679c\u786e\u8ba4\u4f60\u7684\u4ee3\u7801\u65e0bug\uff0c\u90a3\u4e48\u539f\u56e0\u53ea\u6709\u4e00\u4e2a\uff0c\u5c31\u662f\u4f60\u6240\u8c03\u7684\u7f51\u7edc\u8fd8\u4e0d\u591f\u597d(orz)\uff01<\/p>\n<p>\u5728\u8c03\u8bd5\u795e\u7ecf\u7f51\u7edc\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6709\u592a\u591a\u4e0d\u786e\u5b9a\u7684\u56e0\u7d20\u9700\u8981\u4f60\u53bb\u4ed4\u7ec6\u601d\u8003\u5e76\u5c0f\u5fc3\u7ffc\u7ffc\u5730\u53bb\u8c03\u8bd5\uff0c\u800c\u8fd9\u4e9b\u5927\u90e8\u5206\u90fd\u9700\u8981\u9760\u76f4\u89c9\u3001\u7ecf\u9a8c\u548c\u5c11\u8bb8\u8fd0\u6c14\u6765\u8c03\u8bd5\u51b3\u5b9a\u7684\uff0c\u6bd4\u5982\uff1a<\/p>\n<p>(1)  \u9700\u8981\u9009\u53d6\u591a\u5927\u7684\u795e\u7ecf\u7f51\u7edc\uff08\u4e5f\u5c31\u662f\u9009\u7528\u4ec0\u4e48\u6837\u7684\u62df\u5408\u51fd\u6570\uff09\uff1f\u5177\u4f53\u5730\uff0c\u7f51\u7edc\u8981\u591a\u5c11\u5c42\uff1f\u6bcf\u5c42\u591a\u5c11\u8282\u70b9\uff1f\u8fd9\u4e2a\u53ea\u80fd\u51ed\u76f4\u89c9\u6216\u7ecf\u9a8c\u4e86\u3002\u7b80\u5355\u70b9\u7684\u8bdd\uff0c\u5c31\u5957\u7528\u73b0\u6210\u7684\u7f51\u7edc\u7ed3\u6784\uff0c\u6216\u8005\u518d\u7ecf\u8fc7\u4e00\u4e9b\u4fee\u6539\u5373\u53ef\u3002\u4ece\u51fd\u6570\u7684\u81ea\u7531\u5ea6\u6765\u770b\uff0c\u7f51\u7edc\u7684\u53c2\u6570\u4e2a\u6570\u4e0e\u6570\u636e\u5927\u5c0f\u4e0d\u5e94\u76f8\u5dee\u592a\u5927\u3002<\/p>\n<p>(2)  \u521d\u59cb\u5316\u3002\u5bf9\u4e8e\u9ad8\u5ea6\u975e\u7ebf\u6027\u7684\u51fd\u6570\u7684\u6700\u4f18\u5316\uff0c\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u56e0\u7d20\u5c31\u662f\u5982\u4f55\u6311\u9009\u4e00\u4e2a\u597d\u7684\u521d\u59cb\u5316\uff1f<\/p>\n<p>(3)  \u5728\u4f18\u5316\u8fc7\u7a0b\u4e2d\uff0c\u5982\u4f55\u5224\u65ad\u4f18\u5316\u8fc7\u7a0b\u662f\u5426\u6536\u655b\uff1f<\/p>\n<p>(4)  \u662f\u5426\u53d1\u751f\u4e86\u8fc7\u62df\u5408\uff1f<\/p>\n<p>(5)  \u2026 \u2026.<\/p>\n<p>\u4ee5\u4e0b\u6709\u4e9b\u7b80\u5355\u7684\u5c0f\u7ecf\u9a8c\u5206\u4eab\u4e0b\uff1a<\/p>\n<p>(1)  \u4e00\u5b9a\u8981\u53ef\u89c6\u5316\u4f60\u7684\u7ed3\u679c\uff01\u8fd9\u6837\u6709\u52a9\u4e8e\u4f60\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u53d1\u73b0\u95ee\u9898\u3002\u4f60\u5e94\u8be5\u660e\u786e\u7684\u770b\u5230\u8fd9\u4e9b\u6570\u636e\uff1a\u635f\u5931\u51fd\u6570\u7684\u53d8\u5316\u66f2\u7ebf\u3001\u6743\u91cd\u76f4\u65b9\u56fe\u3001\u53d8\u91cf\u7684\u68af\u5ea6\u7b49\u3002\u4e0d\u80fd\u53ea\u770b\u6570\u503c\uff0c\u4e00\u5b9a\u8981\u53ef\u89c6\u5316\uff01<\/p>\n<p>(2)  \u7f51\u7edc\u4e0d\u662f\u8d8a\u6df1\u8d8a\u597d\uff01\u4e0d\u8981\u4e00\u4e0a\u6765\u5c31\u7528VGG19, ResNet50\u7b49\u6807\u51c6\u7684\u5927\u7f51\u7edc\uff0c\u53ef\u80fd\u4f60\u7684\u95ee\u9898\u53ea\u8981\u51e0\u5c42\u5c31\u80fd\u89e3\u51b3\u95ee\u9898\u3002<\/p>\n<p>(3)  \u5148\u5efa\u7acb\u4e00\u4e2a\u8f83\u5c0f\u7684\u7f51\u7edc\u6765\u89e3\u51b3\u6838\u5fc3\u95ee\u9898\uff0c\u7136\u540e\u4e00\u6b65\u4e00\u6b65\u6269\u5c55\u5230\u5168\u5c40\u95ee\u9898\u3002<\/p>\n<p>(4)  \u5148\u7528\u5c0f\u6837\u672c\u505a\u8bad\u7ec3\uff0c\u6709\u4e86\u611f\u89c9\u540e\uff0c\u518d\u8c03\u8bd5\u5927\u7684\u8bad\u7ec3\u6570\u636e\u3002<\/p>\n<p>(5)  \u5982\u679c\u5728\u51e0\u767e\u6b21\u8fed\u4ee3\u540e\uff0c\u8fed\u4ee3\u8fd8\u6ca1\u5f00\u59cb\u6536\u655b\uff0c\u90a3\u4e48\u5c31\u8981\u7ec8\u6b62\u8fed\u4ee3\uff0c\u4e0d\u8981\u50bb\u7b49\u4e86\uff01\u8981\u8003\u8651\u4fee\u6539\u4f60\u7684\u7f51\u7edc\u4e86\u3002<\/p>\n<p>(6)  \u6ce8\u610f\u907f\u514d\u68af\u5ea6\u6d88\u5931\u6216\u68af\u5ea6\u7206\u70b8\u3002<\/p>\n<p>(7)  \u53e6\u5916\uff0c\u5728\u4e92\u8054\u7f51\u4e0a\u8fd8\u80fd\u627e\u5230\u8bb8\u591a\u7f51\u53cb\u4eec\u5206\uff08tu3\uff09\u4eab\uff08cao2\uff09\u7684\u5b9e\u7528\u8c03\u7f51\u7edc\u7684\u7ecf\u9a8c\uff0c\u8bfb\u8005\u53ef\u81ea\u884c\u53bb\u67e5\u627e\u5b66\u4e60\u3002<\/p>\n<p>\u503c\u5f97\u63d0\u9192\u7684\u662f\uff0c\u4e0a\u8ff0\u5206\u4eab\u7684\u5404\u4e2a\u7ecf\u9a8c\u6ca1\u6709\u7edd\u5bf9\u7684\u5bf9\u4e0e\u9519\uff0c\u987b\u5c06\u5b83\u4eec\u5f53\u4f5c\u7ecf\u9a8c\u53bb\u5b66\u4e60\u548c\u4f7f\u7528\u5373\u53ef\u3002\u9700\u8981\u6839\u636e\u4f60\u81ea\u5df1\u7684\u5b9e\u9645\u95ee\u9898\u6765\u8bbe\u8ba1\u548c\u8c03\u8bd5\u4f60\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n<p>\u5373\u4fbf\u5bf9\u4e8e\u884c\u5bb6\u6765\u8bf4\uff0c\u8c03\u8bd5\u8f83\u5927\u7684\u795e\u7ecf\u7f51\u7edc\u4e5f\u662f\u4e00\u9879\u8270\u5de8\u7684\u4efb\u52a1\u3002\u6570\u767e\u4e07\u4e2a\u53c2\u6570\u5728\u4e00\u8d77\u51b3\u5b9a\u7684\u51fd\u6570\uff0c\u4e00\u4e2a\u5fae\u5c0f\u7684\u53d8\u5316\u5c31\u80fd\u6bc1\u6389\u6240\u6709\u8f9b\u52e4\u5de5\u4f5c\u7684\u6210\u679c\u3002\u7136\u800c\u4e0d\u8fdb\u884c\u8c03\u8bd5\u4ee5\u53ca\u53ef\u89c6\u5316\uff0c\u4e00\u5207\u5c31\u53ea\u80fd\u9760\u8fd0\u6c14\uff0c\u6700\u540e\u53ef\u80fd\u6d6a\u8d39\u6389\u5927\u628a\u7684\u9752\u6625\u5c81\u6708\u3002<\/p>\n<p>\u6b63\u56e0\u4e3a\u8fd9\u4e9b\u539f\u56e0\uff0c\u8c03\u8bd5\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u88ab\u8ba4\u4e3a\u662f\u4e2a\u4e0d\u53ef\u89e3\u91ca\u7684\u201c\u9ed1\u7bb1\u5b50\u201d\uff0c\u4f18\u5316\u7f51\u7edc\u7684\u8fc7\u7a0b\u6210\u4e3a\u201c\u8c03\u53c2\u201d\uff0c\u4e5f\u88ab\u620f\u79f0\u4e3a\u201c\u70bc\u4e39\u201d\uff0c\u662f\u4e2a\u9700\u8981\u4e30\u5bcc\u7ecf\u9a8c\u7684\u201c\u6280\u672f\u6d3b\u201d\u3002<\/p>\n<p>9.3.      \u6df1\u5ea6\u5b66\u4e60\u5f00\u53d1\u5de5\u5177<\/p>\n<p>\u8981\u5b66\u4e60\u548c\u4f7f\u7528\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\uff0c\u95e8\u69db\u5e76\u4e0d\u9ad8\u3002\u4f60\u5927\u4e0d\u5fc5\u4ece\u5934\u5f00\u59cb\u81ea\u5df1\u642d\u5efa\u795e\u7ecf\u7f51\u7edc\u7cfb\u7edf\u548c\u5b9e\u73b0\u4f18\u5316\u7b97\u6cd5\u3002\u8fd1\u51e0\u5e74\u6765\uff0c\u5f88\u591a\u5927\u516c\u53f8\u548c\u79d1\u7814\u673a\u6784\u90fd\u5728\u7814\u7a76\u81ea\u5df1\u7684\u6df1\u5ea6\u5b66\u4e60\u6846\u67b6\uff0c\u4e14\u63a8\u51fa\u4e86\u4e0d\u5c11\u6df1\u5ea6\u5b66\u4e60\u5f00\u53d1\u5e73\u53f0\uff08\u5982\u56fe27\uff09\uff0c\u6df1\u5ea6\u5b66\u4e60\u7684\u5f00\u53d1\u6846\u67b6\u548c\u5de5\u5177\u4e5f\u8d8a\u6765\u8d8a\u591a\uff0c\u4f7f\u5f97\u5e94\u7528\u6df1\u5ea6\u5b66\u4e60\u7684\u5165\u95e8\u95e8\u69db\u8d8a\u6765\u8d8a\u4f4e\u3002\u4f7f\u7528\u597d\u7684\u5f00\u53d1\u5de5\u5177\uff0c\u53ef\u8ba9\u4f7f\u7528\u8005\u51cf\u5c11\u5e95\u5c42\u5f00\u53d1\u7684\u5de5\u4f5c\u91cf\uff0c\u800c\u5c06\u91cd\u70b9\u5173\u6ce8\u4e8e\u6df1\u5ea6\u5b66\u4e60\u5e94\u7528\u903b\u8f91\u7684\u5f00\u53d1\u53ca\u6a21\u578b\u7684\u4f18\u5316\u4e0a\uff0c\u63d0\u9ad8\u5f00\u53d1\u6548\u7387\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image170.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe27. \u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u5f00\u53d1\u5de5\u5177\u3002\uff08\u56fe\u7247\u6765\u81ea\u4e92\u8054\u7f51\uff09<\/p>\n<p>\u8fd9\u91cc\u7b80\u5355\u4ecb\u7ecd\u51e0\u6b3e\u5927\u5bb6\u5e38\u7528\u7684\u6df1\u5ea6\u5b66\u4e60\u5f00\u53d1\u5de5\u5177\u5305\uff0c\u57fa\u672c\u90fd\u662f\u5f00\u6e90\u7684\u3002<\/p>\n<p>(1)  TensorFlow, \u7531Google\u516c\u53f8\u53d1\u5e03\u3002\u652f\u6301\u591aCPU\u53ca\u591aGPU\u5e76\u884c\u5316\u8fd0\u884c\uff0c\u5e76\u652f\u6301CNN\uff0cRNN\u7b49\u4e3b\u8981\u7684\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u3002Github\u793e\u533a\u4eba\u6c14\u6700\u706b\u7684\u6df1\u5ea6\u5b66\u4e60\u5f00\u6e90\u9879\u76ee\u3002<\/p>\n<p>(2)  Caffe\uff0c\u7531\u52a0\u62ff\u5927Berkeley BVLC\u5b9e\u9a8c\u5ba4\u53d1\u5e03\u3002\u4f7f\u7528\u6700\u5e7f\u6cdb\u7684\u6df1\u5ea6\u5b66\u4e60\u5de5\u5177\u4e4b\u4e00\uff0c\u63d0\u4f9bC++\uff0cPython\uff0cMatlab\u7b49\u8bed\u8a00\u63a5\u53e3\u3002<\/p>\n<p>(3)  Torch\uff0c\u57fa\u4e8e Lua \u811a\u672c\u8bed\u8a00\u7684\u5de5\u5177\uff0c\u652f\u6301 iOS\u3001 Android \u7b49\u5d4c\u5165\u5f0f\u5e73\u53f0\u3002<\/p>\n<p>(4)  Theano\uff0c\u57fa\u4e8ePython\u8bed\u8a00\u5f00\u53d1\u7684\u6df1\u5ea6\u5b66\u4e60\u5f00\u6e90\u4eff\u771f\u5e73\u53f0\u3002<\/p>\n<p>(5)  Keras\uff0c\u57fa\u4e8ePython\u8bed\u8a00\u5f00\u53d1\u7684\uff0c\u5e95\u5c42\u5e93\u4f7f\u7528Theano\u6216TensorFlow\u3002\u5176\u6a21\u5757\u5316\u7279\u6027\u975e\u5e38\u9002\u5408\u521a\u5165\u95e8\u7684\u521d\u5b66\u8005\u5feb\u901f\u5b9e\u9a8c\u5e76\u6d4b\u8bd5\u6df1\u5ea6\u5b66\u4e60\u7f51\u7edc\u7684\u6027\u80fd\uff0c\u540c\u65f6\u4e5f\u5f00\u653e\u63d0\u4f9b\u5bf9\u5e95\u5c42\u7684\u4fee\u6539\u3002<\/p>\n<p>\u5173\u4e8e\u8fd9\u4e9b\u5f00\u53d1\u5de5\u5177\u5305\u7684\u4f7f\u7528\uff0c\u4e92\u8054\u7f51\u4e0a\uff08\u5305\u62ecGithub\uff09\u6709\u975e\u5e38\u4e30\u5bcc\u7684\u6559\u6750\u548c\u4f7f\u7528\u6587\u6863\uff0c\u8bfb\u8005\u6709\u5174\u8da3\u53ef\u4ee5\u81ea\u884c\u67e5\u9605\u5b66\u4e60\u3002<\/p>\n<p>9.4.      \u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e13\u7528\u82af\u7247<\/p>\n<p>\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e13\u7528\u82af\u7247\uff08\u4f7f\u7528GPU+DNN\u7684\u4e13\u7528\u82af\u7247\uff09\u662f\u4e00\u79cd\u7279\u6b8a\u7528\u9014\u7684\u5904\u7406\u5668\uff0c\u5b83\u80fd\u591f\u4f7f\u5f97\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u66f4\u5feb\uff0c\u5177\u6709\u66f4\u9ad8\u7684\u6027\u80fd\u548c\u66f4\u4f4e\u7684\u529f\u8017\u3002DNN \u4e13\u7528\u82af\u7247\u5728\u6027\u80fd\u548c\u80fd\u6e90\u6d88\u8017\u65b9\u9762\u7684\u597d\u5904\u662f\u663e\u8457\u7684\uff0cDNN\u4e13\u7528\u82af\u7247\u7684\u5e7f\u6cdb\u4f7f\u7528\u8fd8\u9700\u8981\u795e\u7ecf\u7f51\u7edc\u4f53\u7cfb\u7ed3\u6784\u7684\u6807\u51c6\u5316\u548c\u5bf9\u4e0d\u540cDNN\u6846\u67b6\u7684\u652f\u6301\u3002\u56fd\u5916\u7684\u4e00\u4e9b\u516c\u53f8\uff0c\u5305\u62ecGoogle\u3001Nvidia\u3001Intel\u7b49\u516c\u53f8\uff0c\u5df2\u7ecf\u5f00\u53d1\u548c\u90e8\u7f72\u4e86DNN\u4e13\u7528\u82af\u7247\uff0c\u4e3a\u57fa\u4e8eDNN\u7684\u5e94\u7528\u7a0b\u5e8f\u63d0\u4f9b\u4e86\u6781\u9ad8\u7684\u6027\u80fd\u3002\u56fd\u5185\u4e5f\u6709\u4e0d\u5c11\u516c\u53f8\uff08\u5982\u5bd2\u6b66\u7eaa\u3001\u963f\u91cc\u5df4\u5df4\u7b49\uff09\u5728\u4ece\u4e8bDNN\u4e13\u7528\u82af\u7247\u7684\u7814\u53d1\uff0c\u4e5f\u5df2\u7ecf\u8fbe\u5230\u56fd\u9645\u524d\u6cbf\u6c34\u5e73\u3002<\/p>\n<h2><strong>\u5341\u3001<\/strong>  <strong>\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u80fd\u529b\u4e0e\u5c40\u9650<\/strong><\/h2>\n<p>\u6df1\u5ea6\u5b66\u4e60\u771f\u6709\u667a\u80fd\u5417\uff1f\u9057\u61be\u7684\u662f\uff0c\u6ca1\u6709\uff01<\/p>\n<p>10.1.    \u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u672c\u8d28\u518d\u56de\u987e<\/p>\n<p>\u5728\u672c\u6587\uff0c\u7b14\u8005\u4ece\u51fd\u6570\u903c\u8fd1\u8bba\u7684\u89d2\u5ea6\u5df2\u8be6\u7ec6\u5256\u6790\u4e86\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\uff0c\u5f52\u7eb3\u4e3a\u4ee5\u4e0b4\u4e2a\u57fa\u672c\u70b9\uff1a<\/p>\n<p>(1)  \u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff08DNN\uff09\u662f\u4e00\u4e2a\u590d\u5408\u51fd\u6570\u3002\u5bf9\u4e8e\u4efb\u4f55\u5355\u53d8\u91cf\u51fd\u6570\uff0c\u53ea\u8981\u795e\u7ecf\u5143\u8db3\u591f\u591a\uff0c\u795e\u7ecf\u7f51\u7edc\u51fd\u6570\u5c31\u80fd\u4efb\u610f\u903c\u8fd1\u5b83\uff1b\u5bf9\u4e8e\u4efb\u4f55\u591a\u53d8\u91cf\u51fd\u6570\uff0c\u4e00\u5b9a\u53ef\u4ee5\u88ab\u591a\u4e2a\u5355\u53d8\u91cf\u51fd\u6570\u7684\u590d\u5408\u6765\u903c\u8fd1\uff0c\u56e0\u6b64\u5c31\u80fd\u88ab\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u51fd\u6570\u8fdb\u884c\u903c\u8fd1\uff1b\u4e0a\u8ff0\u4e24\u70b9\u4e3a\u795e\u7ecf\u7f51\u7edc\u51fd\u6570\u7684\u8868\u8fbe\u80fd\u529b\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\uff1b<\/p>\n<p>(2)  \u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\u662f\u4e2a\u6570\u636e\u62df\u5408\uff08\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52\uff09\u7684\u8fc7\u7a0b\uff1b<\/p>\n<p>(3)  \u62df\u5408\u8fc7\u7a0b\u662f\u5728\u5b66\u4e60\u57fa\u51fd\u6570\uff1b<\/p>\n<p>(4)  \u591a\u5c42\u6620\u5c04\u662f\u5728\u505a\u591a\u6b21\u53d8\u6362\uff08\u6216\u53c2\u6570\u5316\uff09\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\u662f\u53ef\u4ee5\u5f88\u6e05\u695a\u88ab\u7406\u89e3\u7684\uff01\u5177\u4f53\u7684\u5e94\u7528\u8fc7\u7a0b\u4e2d\uff0c\u9009\u591a\u5c11\u5c42\u3001\u9009\u591a\u5c11\u57fa\u7684\u95ee\u9898\u5728\u903c\u8fd1\u8bba\u4e2d\u5c31\u662f\u6ca1\u6709\u5f88\u597d\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u8fd9\u662f\u903c\u8fd1\u8bba\u4e2d\u5c31\u5b58\u5728\u7684\u95ee\u9898\uff0c\u5e76\u4e0d\u662f\u6df1\u5ea6\u7f51\u7edc\u5e26\u6765\u7684\u95ee\u9898\uff01<\/p>\n<p>\u4ece\u6570\u5b66\u672c\u8d28\u6765\u770b\uff0c\u6df1\u5ea6\u5b66\u4e60\u662f\u5728\u505a\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52\uff1b\u5176\u4ed6\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u4e5f\u662f\u57fa\u4e8e\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52\u7684\u5176\u4ed6\u56de\u5f52\u65b9\u6cd5\u6216\u8005\u7edf\u8ba1\u65b9\u6cd5\u3002<\/p>\n<p>\u4ece\u5e94\u7528\u6027\u6765\u770b\uff0c\u8fd8\u6709\u4ee5\u4e0b\u4e00\u4e9b\u5bf9\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u672c\u8d28\u7684\u8bf4\u660e\uff1a<\/p>\n<p>(1)  \u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\u5b9e\u9645\u4e0a\u5728\u505a\u62df\u5408\u548c\u7edf\u8ba1\uff0c\u7f51\u7edc\u7ed3\u6784\u8bbe\u8ba1\u9700\u8981\u9760\u76f4\u89c9\u3001\u6280\u5de7\u548c\u7ecf\u9a8c\u4ee5\u53ca\u8fd0\u6c14\uff1b<\/p>\n<p>(2)  \u6fc0\u6d3b\u51fd\u6570\u548c\u635f\u5931\u51fd\u6570\u7684\u9009\u62e9\u4e5f\u5f88\u91cd\u8981\uff1b<\/p>\n<p>(3)  DNN\u7684\u5c42\u6570\u3001\u5404\u5c42\u7684\u795e\u7ecf\u5143\u4e2a\u6570\u51b3\u5b9a\u4e86\u8be5\u51fd\u6570\u7684\u53c2\u6570\uff1b\u4e00\u822c\u7684DNN\u90fd\u5177\u6709\u975e\u5e38\u591a\u7684\u53c2\u6570\uff1b<\/p>\n<p>(4)  DNN\u9002\u5408\u62df\u5408\u5927\u89c4\u6a21\u6570\u636e\uff1b\u5bf9\u5c0f\u89c4\u6a21\u6570\u636e\uff0c\u4e0d\u5efa\u8bae\u7528DNN\uff1b<\/p>\n<p>(5)  \u4efb\u4f55\u4e00\u4e2a\u4e2d\u95f4\u9690\u5c42\u7684\u8f93\u51fa\u5411\u91cf\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u8f93\u5165\u6570\u636e\u7684\u7279\u5f81\uff08\u5728\u8be5\u7ef4\u6570\u4e0a\u7684\uff09\uff0c\u4e5f\u662f\u8f93\u5165\u6570\u636e\u7684\u53c2\u6570\u5316\uff1b<\/p>\n<p>(6)  DNN\u53ef\u4ee5\u4efb\u610f\u62fc\u88c5\u3001\u7ec4\u5408\u6210\u5404\u79cd\u590d\u6742\u7684\u7f51\u7edc\u7ed3\u6784\uff1b<\/p>\n<p>(7)  \u5927\u90e8\u5206\u8bba\u6587\u4e2d\u7684DNN\u7ed3\u679c\u90fd\u53ef\u80fd\u662f\u8fc7\u62df\u5408\uff1b\u56e0\u6b64\uff0c\u5f88\u5bb9\u6613\u51fa\u73b0\u8bef\u5224\u7684\u60c5\u51b5\uff08\u8f93\u5165\u7684\u8f7b\u5fae\u53d8\u5316\uff0c\u6bd4\u5982\u7ed9\u56fe\u7247\u52a0\u5c11\u91cf\u566a\u58f0\uff0c\u7ed3\u679c\u5c31\u76f8\u5dee\u5f88\u5927\uff09\uff0c\u5bb9\u6613\u72af\u5927\u9519\uff1b<\/p>\n<p>(8)  DNN\u662f\u4ee5\u6210\u8d25\u8bba\u82f1\u96c4\u7684\uff0c\u9700\u8981\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u597d\u624d\u662f\u771f\u7684\u597d\uff0c\u800c\u8fd9\u4e2a\u6c38\u8fdc\u4e0d\u77e5\u9053\u3002<\/p>\n<p>\u9700\u8981\u518d\u63d0\u4e00\u4e0b\u7684\u662f\uff0c\u672c\u6587\u6240\u8ba8\u8bba\u7684\u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\u53ea\u662f\u6df1\u5ea6\u5b66\u4e60\u7684\u4e00\u79cd\u65b9\u6cd5\u800c\u5df2\u3002\u8fd8\u6709\u5176\u4ed6\u7684\u6df1\u5ea6\u5b66\u4e60\uff0c\u6bd4\u5982\u5357\u4eac\u5927\u5b66\u5468\u5fd7\u534e\u8001\u5e08\u56e2\u961f\u6240\u63d0\u7684\u6df1\u5ea6\u68ee\u6797\u7b49\u65b9\u6cd5\u3002<\/p>\n<p>10.2.    \u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u5177\u6709\u201c\u667a\u80fd\u201d\u5417\uff1f<\/p>\n<p>\u4ece\u4e0a\u9762\u7684\u5256\u6790\u6765\u770b\uff0c\u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\u5b9e\u8d28\u4e0a\u5c31\u662f\u5bf9\u6837\u672c\u6570\u636e\u96c6\u7684\u62df\u5408\u800c\u5df2\uff01\u663e\u800c\u6613\u89c1\uff0c\u5b83\u4ec5\u4ec5\u662f\u4e00\u4e2a\u7531\u6570\u636e\u9a71\u52a8\u7684\u4ea7\u751f\u7684\u62df\u5408\u5668\u6216\u5206\u7c7b\u5668\uff0c\u6839\u672c\u4e0d\u662f\u4e00\u4e2a\u201c\u8ba4\u77e5\u7cfb\u7edf\u201d\uff01\u6211\u4eec\u5e76\u6ca1\u6709\u770b\u51fa\u6765\u5b83\u6709\u4efb\u4f55\u201c\u667a\u80fd\u201d\uff08\u5373\u5bf9\u6570\u636e\u6240\u5448\u73b0\u7684\u89c4\u5f8b\u3001\u77e5\u8bc6\u7684\u7406\u89e3\uff09\u7684\u5b58\u5728\uff01\u5bf9\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u7814\u7a76\u53ef\u80fd\u4ecd\u7136\u662f\u51e0\u5341\u5e74\u524d\u7684\u8fdb\u5c55\uff0c\u53ea\u4e0d\u8fc7\u73b0\u5728\u7f51\u7edc\u7684\u89c4\u6a21\u53d8\u5927\u4e86\uff08\u6570\u636e\u5927\u4e86\uff0c\u4f18\u5316\u5f3a\u4e86\uff09\u800c\u5df2\uff01<\/p>\n<p>\u4ece\u903c\u8fd1\u8bba\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u5982\u679c\u6570\u636e\u8db3\u591f\u5927\uff0c\u591a\u5230\u8db3\u4ee5\uff08\u7a20\u5bc6\uff09\u8986\u76d6\u6574\u4e2a\u76ee\u6807\u51fd\u6570\uff0c\u90a3\u4e48\u7b80\u5355\u7684\u6700\u8fd1\u90bb\u67e5\u627e\u6216\u8005\u5c40\u90e8\u7ebf\u6027\u63d2\u503c\u7684\u6027\u80fd\u5c31\u8db3\u591f\u597d\u4e86\u3002\u6b64\u65f6\uff0c\u7b14\u8005\u731c\u6d4b\uff0c\u6df1\u5ea6\u5b66\u4e60\u7684\u6027\u80fd\u4e0e\u6700\u8fd1\u90bb\u67e5\u627e\u7684\u6027\u80fd\u53ef\u80fd\u76f8\u5dee\u65e0\u51e0\uff01<\/p>\n<p>\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u5e02\u9762\u4e0a\u51fa\u73b0\u4e86\u8bb8\u591a\u79cd\u7c7b\u7684\u6240\u8c13\u7684\u201c\u667a\u80fd\u673a\u5668\u4eba\u201d\uff0c\u58f0\u79f0\u53ef\u4ee5\u4e0e\u4eba\u8fdb\u884c\u81ea\u7531\u5bf9\u8bdd\u3002\u5efa\u8bae\u8bfb\u8005\u53bb\u6d4b\u8bd5\u4e00\u4e0b\u8fd9\u4e9b\u5bf9\u8bdd\u673a\u5668\u4eba\uff0c\u4f60\u4eec\u5c31\u4f1a\u53d1\u73b0\uff0c\u8fd9\u4e9b\u673a\u5668\u4eba\u7684\u95ee\u7b54\u7cfb\u7edf\u57fa\u672c\u6ca1\u6709\u7406\u89e3\uff08\u53ea\u6709\u5c11\u6570\u6709\u5c11\u91cf\u7b80\u5355\u7684\u7406\u89e3\uff09\u3002\u5982\u679c\u5bf9\u4e8e\u5728\u5176\u6570\u636e\u5e93\u4e2d\u5b58\u5728\u7684\u95ee\u9898\u6216\u7c7b\u4f3c\u7684\u95ee\u9898\uff0c\u673a\u5668\u4eba\u80fd\u591f\u56de\u7b54\u5f97\u6bd4\u8f83\u5408\u7406\uff1b\u5982\u679c\u9047\u4e0a\u9700\u8981\u903b\u8f91\u63a8\u7406\u7684\u95ee\u9898\uff0c\u8fd9\u4e9b\u673a\u5668\u4eba\u57fa\u672c\u5c31\u7b54\u975e\u6240\u95ee\uff0c\u6216\u8005\u738b\u987e\u5de6\u53f3\u800c\u8a00\u4ed6\uff0c\u751a\u81f3\u5f00\u59cb\u201c\u5356\u840c\u201d\u4e86\u3002\u6709\u7a7a\u53bb\u9017\u9017\u8fd9\u4e9b\u5bf9\u8bdd\u673a\u5668\u4eba\u4e5f\u662f\u86ee\u6709\u610f\u601d\u7684\u4e8b\u3002<\/p>\n<p>\u5bf9\u4e8e\u81ea\u52a8\u7ffb\u8bd1\u7b49\u673a\u5668\u4eba\uff0c\u53ea\u8981\u6709\u8db3\u591f\u7684\u4e24\u79cd\u8bed\u8a00\u7684\u5bf9\u5e94\u8bcd\u6761\u6216\u53e5\u5b50\uff08\u6bd4\u5982\u6709\u4e9b\u516c\u53f8\u7684\u8bcd\u5e93\u6570\u636e\u5e93\u975e\u5e38\u5e9e\u5927\uff0c\u8fbe\u5230\u4ebf\u7ea7\uff09\uff0c\u5c31\u80fd\u201c\u7ffb\u8bd1\u201d\uff08\u62df\u5408\uff09\u5f97\u8fd8\u4e0d\u9519\uff0c\u8fbe\u5230\u4e00\u5b9a\u7684\u5b9e\u7528\u6c34\u51c6\u3002\u4f46\u4ece\u672c\u8d28\u4e0a\u6765\u8bb2\uff0c\u8fd9\u4e9b\u7ffb\u8bd1\u7b97\u6cd5\u5e76\u6ca1\u6709\u771f\u6b63\u7406\u89e3\u8bed\u8a00\u672c\u8eab\uff01<\/p>\n<p>\u5173\u4e8e\u6df1\u5ea6\u5b66\u4e60\uff0c\u6211\u4eec\u8981\u6709\u6e05\u9192\u7684\u8ba4\u8bc6\uff1a<\/p>\n<p>\\1)   \u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u9700\u8981\u5927\u91cf\u7684\u8bad\u7ec3\u6570\u636e\uff0c\u624d\u80fd\u6709\u8f83\u597d\u7684\u6548\u679c\uff1b\u56e0\u4e3a\u8fd9\u4e9b\u5b66\u4e60\u6a21\u578b\u90fd\u5728\u505a\u6570\u636e\u62df\u5408\u6216\u56de\u5f52\uff0c\u6216\u8005\u662f\u5728\u505a\u7edf\u8ba1\uff1b<\/p>\n<p>\\2)   \u5b9e\u9645\u95ee\u9898\u4e2d\uff0c\u5f80\u5f80\u4f1a\u9047\u5230\u5c0f\u6837\u672c\u95ee\u9898\uff0c\u91c7\u7528\u4f20\u7edf\u7684\u7b80\u5355\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\uff0c\u5219\u53ef\u4ee5\u5f88\u597d\u5730\u89e3\u51b3\u4e86\uff0c\u6ca1\u5fc5\u8981\u975e\u5f97\u7528\u590d\u6742\u7684\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\uff1b<\/p>\n<p>\\3)   \u795e\u7ecf\u7f51\u7edc\u770b\u8d77\u6765\u6765\u6e90\u4e8e\u4eba\u8111\u795e\u7ecf\u5143\u7684\u542f\u53d1\uff0c\u4f46\u7edd\u4e0d\u662f\u4eba\u8111\u7684\u6a21\u62df\uff01\u5b83\u53ea\u662f\u4e00\u4e2a\u590d\u5408\u51fd\u6570\uff01\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u7ed9\u4e00\u4e2a\u4e09\u56db\u5c81\u7684\u5c0f\u5b69\u770b\u8fc7\u51e0\u53ea\u732b\u4e4b\u540e\uff0c\u4ed6\u5c31\u80fd\u8bc6\u522b\u5176\u4ed6\u7684\u732b\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4eba\u7c7b\u7684\u5b66\u4e60\u8fc7\u7a0b\u5f80\u5f80\u4e0d\u9700\u8981\u5927\u89c4\u6a21\u7684\u8bad\u7ec3\u6570\u636e\uff0c\u800c\u73b0\u5728\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\u65b9\u6cd5\u663e\u7136\u4e0d\u662f\u5bf9\u4eba\u8111\u7684\u6a21\u62df\u3002<\/p>\n<p>\u8fd9\u51e0\u5e74\u5404\u79cd\u5a92\u4f53\u7684\u5927\u91cf\u5938\u5f20\u7684\u62a5\u9053\u548c\u5ba3\u4f20\uff08\u5373\u4f7f\u662f\u6218\u80dc\u4eba\u7c7b\u7684\u56f4\u68cb\u7b97\u6cd5AlphaGo\uff0c\u4e5f\u5e76\u4e0d\u662f\u771f\u6b63\u7684\u4eba\u5de5\u667a\u80fd\uff0c\u800c\u4ec5\u4ec5\u662f\u673a\u5668\u5728\u4e00\u5b9a\u7684\u6e38\u620f\u89c4\u5219\u4e0b\u7684\u7b56\u7565\u8ba1\u7b97\u80fd\u529b\uff09\uff0c\u6781\u5ea6\u5938\u5927\u4e86\u4eba\u5de5\u667a\u80fd\u7684\u8fdb\u5c55\uff0c\u8ba9\u5f88\u591a\u5927\u4f17\u8bef\u8ba4\u4e3a\u201c\u5f3a\u4eba\u5de5\u667a\u80fd\u201d\u5df2\u7ecf\u6765\u4e34\uff0c\u751a\u81f3\u4ea7\u751f\u4e0d\u5fc5\u8981\u7684\u6050\u614c\u3002<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u73b0\u5728\u7684\u4eba\u5de5\u667a\u80fd\u7684\u8fdb\u5c55\u4ecd\u7136\u5f88\u5c0f\uff0c\u6b63\u5982\u6e05\u534e\u5927\u5b66\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u9662\u9662\u957f\u5f20\u94b9\u9662\u58eb\u57282018\u5e74\u5168\u7403\u4eba\u5de5\u667a\u80fd\u4e0e\u673a\u5668\u4eba\u5cf0\u4f1a\uff08CCF-GAIR\uff09\u4e0a\u7684\u62a5\u544a\u4e0a\u6240\u6307\u51fa\u7684\uff1a\u201c\u4eba\u5de5\u667a\u80fd\u521a\u521a\u8d77\u6b65\uff0c\u79bb\u771f\u6b63\u7684\u4eba\u5de5\u667a\u80fd\u8fd8\u5f88\u9065\u8fdc\u2026 \u6211\u4eec\u5fc5\u987b\u8d70\u5411\u5177\u6709\u7406\u89e3\u7684\u4eba\u5de5\u667a\u80fd\uff0c\u8fd9\u624d\u662f\u771f\u6b63\u7684\u4eba\u5de5\u667a\u80fd\u3002\u201d<\/p>\n<p>10.3.    \u6df1\u5ea6\u5b66\u4e60\u5728\u5de5\u4e1a\u754c\u7684\u5e94\u7528<\/p>\n<p>\u867d\u7136\u8fd1\u51e0\u5e74\u53d1\u5c55\u8d77\u6765\u7684\u57fa\u4e8eDNN\u7684\u6df1\u5ea6\u5b66\u4e60\u5e76\u672a\u4ea7\u751f\u771f\u6b63\u7684\u667a\u80fd\u3002\u4f46\u7531\u4e8e\u73b0\u5728\u6709\u5927\u91cf\u7684\u6570\u636e\uff0c\u57fa\u4e8e\u6570\u636e\u9a71\u52a8\u7684\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u53ef\u4ee5\u5728\u5f88\u591a\u9886\u57df\u786e\u5b9e\u5f97\u5230\u4e86\u843d\u5730\u7684\u5e94\u7528\u3002\u7279\u522b\u662f\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\uff0c\u6bd4\u5982\u4eba\u8138\u8bc6\u522b\u3001\u56fe\u50cf\u5206\u5272\u4e0e\u8bc6\u522b\u7b49\uff0c\u8be5\u9886\u57df\u505a\u4e86\u5f88\u591a\u5e74\u7684\u4e00\u4e9b\u95ee\u9898\u7684\u7814\u7a76\u5de5\u4f5c\uff0c\u77ac\u95f4\u5c31\u88ab\u6df1\u5ea6\u5b66\u4e60\u6240\u51fb\u8d25\uff01\u6df1\u5ea6\u5b66\u4e60\u53d6\u5f97\u4e86\u5de8\u5927\u7684\u6210\u529f\uff01\u56e0\u6b64\uff0c\u6211\u4eec\u4ecd\u80fd\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u89e3\u51b3\u4e0d\u5c11\u95ee\u9898\u3002<\/p>\n<p>\u8fd1\u51e0\u5e74\uff0c\u50ac\u751f\u4e86\u5927\u91cf\u7684\u4eba\u5de5\u667a\u80fd\u516c\u53f8\uff0c\u5206\u5e03\u5728\u5b89\u9632\u3001\u533b\u7597\u3001\u91d1\u878d\u3001\u667a\u80fd\u673a\u5668\u4eba\u3001\u81ea\u52a8\u9a7e\u9a76\u3001\u667a\u80fd\u82af\u7247\u3001\u667a\u80fd\u5bb6\u5c45\u7b49\u9886\u57df\uff1b\u5404\u9ad8\u6821\u4e5f\u7eb7\u7eb7\u6784\u5efa\u4e86\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u9662\u6216\u5927\u6570\u636e\u5b66\u9662\u7b49\uff1b\u5404\u5b66\u4f1a\u6210\u7acb\u4e86\u4eba\u5de5\u667a\u80fd\u76f8\u5173\u7684\u4e13\u4e1a\u59d4\u5458\u4f1a\uff1b\u56fd\u5bb6\u4e5f\u7eb7\u7eb7\u51fa\u53f0\u4e86\u6709\u5173\u4eba\u5de5\u667a\u80fd\u7684\u653f\u7b56\u4e0e\u6587\u4ef6\uff0c\u5305\u62ec\u300a\u65b0\u4e00\u4ee3\u4eba\u5de5\u667a\u80fd\u53d1\u5c55\u89c4\u5212\u300b\uff0c\u9f13\u52b1\u4eba\u5de5\u667a\u80fd\u65b9\u9762\u7684\u4eba\u624d\u57f9\u517b\uff08\u4ece\u5a03\u5a03\u6293\u8d77\uff09\u548c\u4ea7\u4e1a\u843d\u5730\u3002\u5728\u79d1\u7814\u9886\u57df\uff0c\u5927\u91cf\u7684\u7814\u7a76\u5de5\u4f5c\u8005\u548c\u5b66\u751f\u90fd\u6d8c\u8fdb\u5230\u4eba\u5de5\u667a\u80fd\u9886\u57df\uff0c\u5728\u4e00\u4e9b\u4eba\u5de5\u667a\u80fd\u6216\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\u7684\u4f1a\u8bae\u7684\u6295\u7a3f\u91cf\u8fc5\u901f\u589e\u52a0\uff0c\u53c2\u52a0\u4f1a\u8bae\u7684\u4eba\u6570\u8fbe\u5230\u5386\u53f2\u65b0\u9ad8\u3002<\/p>\n<p>\u4f46\u6b8b\u9177\u7684\u4e8b\u5b9e\u662f\uff0c\u7edd\u5927\u90e8\u5206\u7684\u4eba\u5de5\u667a\u80fd\u516c\u53f8\u90fd\u662f\u201c\u4f2a\u4eba\u5de5\u667a\u80fd\u201d\uff0c\u4ed6\u4eec\u6216\u8005\u4ec5\u4ec5\u5728\u505a\u7740\u6570\u636e\u6807\u6ce8\u7684\u5de5\u4f5c\uff0c\u56e0\u4e3a\u6807\u6ce8\u6570\u636e\u7684\u591a\u5c11\u51b3\u5b9a\u7740\u62df\u5408\u51fd\u6570\u7684\u201c\u667a\u80fd\u201d\uff01\u53e6\u5916\uff0c\u5df2\u7ecf\u6709\u4e9b\u516c\u53f8\u56e0\u672a\u80fd\u627e\u5230\u5408\u9002\u7684\u76c8\u5229\u6a21\u5f0f\u800c\u5012\u95ed\u3002\u524d\u51e0\u5e74\u5bf9\u6df1\u5ea6\u5b66\u4e60\u53ca\u667a\u80fd\u7684\u671f\u671b\u5e76\u672a\u8fbe\u5230\u4eba\u4eec\u53ca\u6295\u8d44\u8005\u7684\u9884\u671f\u76ee\u6807\u3002\u4eca\u5e74\u5e74\u521d\uff0c\u674e\u5f00\u590d\u66fe\u6307\u51fa\uff1a\u201c2018\u5e74\u662fAI\u6ce1\u6cab\u7834\u88c2\u4e4b\u5e74\u201d\u3002<\/p>\n<p>\u4ece\u4e24\u5e74\u524d\u4eba\u5de5\u667a\u80fd\u70ed\u6f6e\u7684\u7206\u53d1\uff0c\u5230\u73b0\u5728\u70ed\u6f6e\u9010\u6e10\u9000\u53bb\uff0c\u4eba\u4eec\u4e5f\u8d8a\u6765\u8d8a\u8d8b\u4e8e\u51b7\u9759\u6765\u8ba4\u8bc6\u4eba\u5de5\u667a\u80fd\uff0c\u5bf9\u5176\u7814\u7a76\u4e0e\u5e94\u7528\u9010\u6e10\u8d8b\u4e8e\u52a1\u5b9e\u3002\u7b14\u8005\u4e5f\u5e0c\u671b\u4eba\u5de5\u667a\u80fd\u80fd\u771f\u6b63\u5feb\u901f\u53d1\u5c55\uff0c\u8ba9\u4eba\u7c7b\u7684\u751f\u6d3b\u53d8\u5f97\u8d8a\u6765\u8d8a\u7f8e\u597d\uff01<\/p>\n<p>10.4.    \u6df1\u5ea6\u5b66\u4e60\u4e0e\u4eba\u5de5\u667a\u80fd\u7684\u5173\u7cfb<\/p>\n<p>1956\u5e74\uff0c\u51e0\u4e2a\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u76f8\u805a\u5728\u8fbe\u7279\u8305\u65af\u4f1a\u8bae\uff0c\u63d0\u51fa\u4e86\u201c\u4eba\u5de5\u667a\u80fd\u201d\uff08Artificial Intelligence\uff0c AI\uff09\u7684\u6982\u5ff5\uff0c\u68a6\u60f3\u7740\u7528\u8ba1\u7b97\u673a\u6765\u6784\u9020\u590d\u6742\u7684\u3001\u62e5\u6709\u4e0e\u4eba\u7c7b\u667a\u6167\u540c\u6837\u672c\u8d28\u7279\u6027\u7684\u673a\u5668\u3002\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u9886\u57df\u8303\u56f4\u5f88\u5e7f\uff0c\u5305\u62ec\u4e13\u5bb6\u7cfb\u7edf\u3001\u673a\u5668\u5b66\u4e60\u3001\u8fdb\u5316\u8ba1\u7b97\u3001\u6a21\u7cca\u903b\u8f91\u3001\u8ba1\u7b97\u673a\u89c6\u89c9\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3001\u63a8\u8350\u7cfb\u7edf\u7b49\uff0c\u5982\u56fe27 \uff08\u5de6\uff09\u3002<\/p>\n<p>\u673a\u5668\u5b66\u4e60\uff08Machine Learning, ML\uff09\u662f\u4e00\u79cd\u5b9e\u73b0\u4eba\u5de5\u667a\u80fd\u7684\u65b9\u6cd5\u3002\u5176\u57fa\u672c\u505a\u6cd5\u662f\u4f7f\u7528\u7b97\u6cd5\u6765\u89e3\u6790\u6570\u636e\u3001\u4ece\u4e2d\u5b66\u4e60\uff0c\u7136\u540e\u5bf9\u771f\u5b9e\u4e16\u754c\u4e2d\u7684\u4e8b\u4ef6\u505a\u51fa\u51b3\u7b56\u548c\u9884\u6d4b\u3002\u4e0e\u4f20\u7edf\u7684\u4e3a\u89e3\u51b3\u7279\u5b9a\u4efb\u52a1\u3001\u786c\u7f16\u7801\u7684\u8f6f\u4ef6\u7a0b\u5e8f\u4e0d\u540c\uff0c\u673a\u5668\u5b66\u4e60\u662f\u7528\u5927\u91cf\u7684\u6570\u636e\u6765\u201c\u8bad\u7ec3\u201d\uff0c\u901a\u8fc7\u5404\u79cd\u7b97\u6cd5\u4ece\u6570\u636e\u4e2d\u5b66\u4e60\u5982\u4f55\u5b8c\u6210\u4efb\u52a1\u3002\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u5305\u62ec\u51b3\u7b56\u6811\u3001\u805a\u7c7b\u3001\u8d1d\u53f6\u65af\u5206\u7c7b\u3001\u652f\u6301\u5411\u91cf\u673a\u3001EM\u3001Adaboost\u7b49\u7b49\u3002\u4ece\u5b66\u4e60\u65b9\u6cd5\u4e0a\u6765\u5206\uff0c\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u53ef\u4ee5\u5206\u4e3a\u76d1\u7763\u5b66\u4e60\uff08\u5982\u5206\u7c7b\u95ee\u9898\uff09\u3001\u65e0\u76d1\u7763\u5b66\u4e60\uff08\u5982\u805a\u7c7b\u95ee\u9898\uff09\u3001\u534a\u76d1\u7763\u5b66\u4e60\u3001\u96c6\u6210\u5b66\u4e60\u3001\u6df1\u5ea6\u5b66\u4e60\u548c\u5f3a\u5316\u5b66\u4e60\u7b49\u3002<\/p>\n<p>\u6df1\u5ea6\u5b66\u4e60\uff08Deep Learning, DL\uff09\u662f\u4e00\u79cd\u5b9e\u73b0\u673a\u5668\u5b66\u4e60\u7684\u6280\u672f\uff0c\u662f\u89e3\u51b3\u7279\u5f81\u8868\u8fbe\u7684\u4e00\u79cd\u5b66\u4e60\u8fc7\u7a0b\u3002\u73b0\u5728\u5e38\u6307\u5229\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u3002\u5728\u5f88\u65e9\u5c31\u6709\u4eba\u63d0\u8fc7\uff0c\u4f46\u7531\u4e8e\u5f53\u65f6\u8bad\u7ec3\u6570\u636e\u91cf\u4e0d\u8db3\u3001\u8ba1\u7b97\u80fd\u529b\u843d\u540e\uff0c\u56e0\u6b64\u6df1\u5ea6\u5b66\u4e60\u7684\u6548\u679c\u4e0d\u5c3d\u5982\u4eba\u610f\uff1b\u76f4\u5230\u8fd1\u51e0\u5e74\uff0c\u6df1\u5ea6\u5b66\u4e60\u624d\u8f83\u597d\u5730\u5b9e\u73b0\u4e86\u5404\u79cd\u4efb\u52a1\u3002\u4e8b\u5b9e\u4e0a\uff0c\u9664\u4e86\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\uff0c\u8fd8\u6709\u5176\u4ed6\u5f62\u5f0f\uff08\u6bd4\u5982\u6df1\u5ea6\u68ee\u6797\uff09\u7684\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u673a\u5668\u5b66\u4e60\u662f\u4e00\u79cd\u5b9e\u73b0\u4eba\u5de5\u667a\u80fd\u7684\u65b9\u6cd5\uff0c\u6df1\u5ea6\u5b66\u4e60\u662f\u4e00\u79cd\u5b9e\u73b0\u673a\u5668\u5b66\u4e60\u7684\u6280\u672f\uff0c\u800c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u662f\u5b9e\u73b0\u6df1\u5ea6\u5b66\u4e60\u7684\u4e00\u79cd\u5177\u4f53\u7684\u5b9e\u73b0\u5de5\u5177\uff0c\u5982\u56fe28\uff08\u53f3\uff09\u6240\u793a\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u4ece\u8303\u7574\u6765\u8bb2\uff0c\u4ed6\u4eec\u7684\u5173\u7cfb\u5982\u4e0b\uff1a<\/p>\n<p>\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc &lt; \u6df1\u5ea6\u5b66\u4e60 &lt; \u673a\u5668\u5b66\u4e60 &lt; \u4eba\u5de5\u667a\u80fd<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image171.jpg\" alt=\"img\" \/> <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image172.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe28. \u5de6\uff1a\u4eba\u5de5\u667a\u80fd\u7684\u7814\u7a76\u8303\u7574\uff1b\u53f3\uff1a\u4eba\u5de5\u667a\u80fd\u3001\u673a\u5668\u5b66\u4e60\u548c\u6df1\u5ea6\u5b66\u4e60\u7684\u5173\u7cfb\u3002<\/p>\n<p>\uff08\u56fe\u7247\u6765\u81ea\u4e92\u8054\u7f51\uff09<\/p>\n<p>\u4f46\u6b8b\u9177\u7684\u4e8b\u5b9e\u662f\uff0c\u8fd1\u51e0\u5e74\u6d41\u884c\u7684\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u4ec5\u4ec5\u662f\u4e00\u4e2a\u6570\u636e\u62df\u5408\u5668\uff0c\u5e76\u4e0d\u5b58\u5728\u7740\u5206\u6790\u4e0e\u7406\u89e3\u7b49\u667a\u80fd\u7684\u80fd\u529b\u3002\u73b0\u6709\u7684\u6280\u672f\u548c\u65b9\u6cd5\u79bb\u771f\u6b63\u7684\u4eba\u5de5\u667a\u80fd\u8fd8\u975e\u5e38\u9065\u8fdc\uff01<\/p>\n<h2><strong>\u5341\u4e00\u3001<\/strong>    <strong>\u4e09\u7ef4\u51e0\u4f55\u6570\u636e<\/strong><\/h2>\n<p>\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0c\u6211\u4eec\u7814\u7a76\u7684\u5bf9\u8c61\u662f\u4e09\u7ef4\uff083D\uff09\u5f62\u72b6\u5bf9\u8c61\uff0c\u5373\u865a\u62df\u7a7a\u95f4\u4e2d\u7684\u6570\u5b57\u5316\u7684\u7269\u7406\u5b9e\u4f53\u3002\u8868\u8fbe3D\u5bf9\u8c61\u76843D\u51e0\u4f55\u6570\u636e\u662f\u7ee7\u58f0\u97f3\u3001\u56fe\u50cf\u3001\u89c6\u9891\u4e4b\u540e\u7684\u7b2c\u56db\u4ee3\u6570\u5b57\u53ef\u89c6\u5a92\u4f53\uff08\u5982\u56fe29\uff09\uff0c\u5df2\u9010\u6e10\u5177\u6709\u8d8a\u6765\u8d8a\u5e7f\u6cdb\u7684\u5e94\u7528\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image173.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe29. \u56db\u4ee3\u53ef\u89c6\u5a92\u4f53\u7684\u53d1\u5c55\uff1a\u58f0\u97f3\u3001\u56fe\u50cf\u3001\u89c6\u9891\u30013D\u51e0\u4f55\u3002<\/p>\n<p>11.1.    3D \u6570\u636e\u7684\u91cd\u8981\u6027<\/p>\n<p>\u5730\u7403\u4e0a\u7684\u4eba\u53ca\u6240\u6709\u52a8\u7269\u90fd\u6709\u4e24\u53ea\u773c\u775b\uff0c\u6bcf\u53ea\u773c\u775b\u7c7b\u4f3c\u4e8e\u4e00\u53f0\u7167\u76f8\u673a\uff0c\u770b\u5230\u7684\u662f\u573a\u666f\u5728\u89c6\u7f51\u819c\uff08\u6210\u50cf\u5e73\u9762\uff09\u4e0a\u7684\u6295\u5f71\u56fe\u50cf\uff0c\u5982\u56fe30\uff08\u5de6\uff09\u3002\u4e24\u53ea\u773c\u775b\u4f4d\u7f6e\u4e0d\u540c\uff0c\u5c31\u4ea7\u751f\u5bf9\u540c\u4e00\u573a\u666f\u7684\u89c6\u5dee\uff0c\u4ece\u800c\u5728\u5927\u8111\u751f\u6210\u4e86\u573a\u666f\u7684\u7acb\u4f53\u548c3D\u4fe1\u606f\uff08\u53cc\u76ee\u7acb\u4f53\u89c6\u89c9\u539f\u7406\uff09\uff0c\u5982\u56fe30\uff08\u53f3\uff09\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image174.jpg\" alt=\"img\" \/> <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image175.png\" alt=\"img\" \/><\/p>\n<p>\u56fe30. \u5de6\uff1a\u5355\u773c\u770b\u5230\u7684\u662f\u56fe\u50cf\uff0c\u4e3a\u4e09\u7ef4\u4e16\u754c\u5728\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u6295\u5f71\u5f71\u50cf\uff1b\u53f3\uff1a\u4eba\u7c7b\u53ca\u52a8\u7269\u7684\u4e24\u53ea\u773c\u775b\u901a\u8fc7\u53cc\u773c\u7684\u89c6\u5dee\u4ea7\u751f\u4e86\u5bf9\u573a\u666f\u7269\u4f53\u7684\u7acb\u4f53\u548c\u4e09\u7ef4\u7684\u4fe1\u606f\u3002\uff08\u56fe\u7247\u6765\u81ea\u4e8e\u4e92\u8054\u7f51\uff09<\/p>\n<p>\u56e0\u6b64\uff0c\u4eba\u7c7b\u53ca\u52a8\u7269\u7684\u89c6\u89c9\u611f\u77e5\u7cfb\u7edf\u662f\u5177\u6709\u7acb\u4f53\u7684\u7279\u6027\u3002\u4e16\u754c\u662f\u4e09\u7ef4\u7684\uff0c3D\u6a21\u578b\u63d0\u4f9b\u4e86\u4e16\u754c\u53ca\u6240\u6709\u7269\u4f53\u7684\u5168\u65b9\u4f4d\u3001\u5168\u606f\u7684\u8868\u8fbe\uff0c\u80fd\u63d0\u4f9b\u6bd4\u4e8c\u7ef4\u56fe\u50cf\u66f4\u4e30\u5bcc\u3001\u66f4\u5168\u9762\u7684\u7a7a\u95f4\u4fe1\u606f\uff08\u6bd4\u5982\u730e\u9e70\u80fd\u5728\u51e0\u516c\u91cc\u5916\u5224\u65ad\u8349\u5730\u4e0a\u4e00\u53ea\u5154\u5b50\u7684\u8fdc\u8fd1\u548c\u65b9\u4f4d\uff0c\u4ee5\u4fbf\u505a\u51fa\u4e0b\u4e00\u6b65\u7684\u98de\u884c\u884c\u4e3a\uff09\u3002\u800c\u5355\u773c\uff08\u5982\u679c\u4ee5\u524d\u5b58\u5728\u7684\u8bdd\uff09\u52a8\u7269\u5219\u56e0\u65e0\u6cd5\u5206\u8fa8\u7269\u4f53\u7684\u8fdc\u8fd1\uff0c\u800c\u65e0\u60c5\u5730\u88ab\u81ea\u7136\u6cd5\u5219\u6240\u6dd8\u6c70\u3002<\/p>\n<p>\u8ba1\u7b97\u673a\u89c6\u89c9\u901a\u8fc7\u5bf9\u56fe\u50cf\u7684\u7406\u89e3\u548c\u5206\u6790\u5df2\u7ecf\u80fd\u591f\u89e3\u51b3\u975e\u5e38\u591a\u7684\u4efb\u52a1\uff08\u6bd4\u5982\u7269\u4f53\u68c0\u6d4b\u3001\u5206\u5272\u3001\u8bc6\u522b\u3001\u68c0\u7d22\u7b49\uff09\u3002\u4f46\u5728\u5f88\u591a\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u679c\u6d89\u53ca\u5230\u7a7a\u95f4\u5173\u7cfb\u5206\u6790\u4ee5\u53ca\u4e0e3D\u73af\u5883\u548c\u7269\u4f53\u7684\u7406\u89e3\u3001\u4ea4\u4e92\u548c\u521b\u9020\uff0c\u5219\u5149\u97602D\u56fe\u50cf\u4fe1\u606f\u662f\u4e0d\u591f\u7684\uff0c\u6b64\u65f6\u5fc5\u987b\u4f9d\u8d56\u573a\u666f\u76843D\u4fe1\u606f\uff0c\u6bd4\u5982\u6570\u5b57\u57ce\u5e02\u4e2d\u7684\u7a7a\u95f4\u5173\u7cfb\u5206\u6790\u3001\u673a\u5668\u4eba\u6293\u53d63D\u7269\u4f53\u3001\u865a\u62df\u548c\u589e\u5f3a\u73b0\u5b9e\u3001\u7269\u8054\u7f51\u6570\u636e\u7684\u7a7a\u95f4\u5173\u8054\u7b49\uff0c\u5982\u56fe31\u6240\u793a\u3002\u5728\u8fd9\u4e9b\u5e94\u7528\u4e2d\uff0c\u4ec5\u4ec5\u9760\u56fe\u50cf\u4fe1\u606f\u662f\u65e0\u6cd5\u5f88\u5feb\u5b8c\u6210\u5404\u9879\u4efb\u52a1\u7684\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image176.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe31. \u4e09\u7ef4\u6570\u636e\u5728\u5f88\u591a\u5b9e\u9645\u5e94\u7528\u573a\u666f\u4e2d\u662f\u5fc5\u4e0d\u53ef\u5c11\u7684\u4fe1\u606f\u3002<\/p>\n<p>11.2.    3D\u6570\u636e\u96c6<\/p>\n<p>\u968f\u77403D\u7269\u4f53\u7684\u626b\u63cf\u4e0e\u91c7\u96c6\u624b\u6bb5\u7684\u65e5\u76ca\u589e\u591a\uff08\u7279\u522b\u662f\u8fd1\u51e0\u5e74\u5feb\u901f\u53d1\u5c55\u7684\u6df1\u5ea6\u76f8\u673a\uff0c\u6bd4\u5982Microsoft Kinect\u3001Intel RealSense\u3001Google Project Tango\u3001Apple Primesense\u3001Asus Xtion\u7b49\uff09\u3001\u672a\u6765\u53ef\u91c7\u96c63D\u4fe1\u606f\u7684\u79fb\u52a8\u7ec8\u7aef\uff08\u53bb\u5e74iPhoneX\u4e0a\u5df2\u6709\u6df1\u5ea6\u76f8\u673a\uff09\u7684\u666e\u53ca\u3001\u4ee5\u53ca\u4e92\u8054\u7f51\u4e0a3D\u6a21\u578b\u7684\u521b\u9020\u4e0e\u5206\u4eab\uff0c3D\u6570\u636e\uff08\u5305\u62ecRGB-D\u6570\u636e\uff09\u5c06\u65e5\u76ca\u4e30\u5bcc\u3002<\/p>\n<p>\u81f3\u4eca\uff0c\u5df2\u6709\u8bb8\u591a\u7814\u7a76\u673a\u6784\u6784\u5efa\u5e76\u516c\u5e03\u4e86\u4e00\u4e9b3D\u6570\u636e\u96c6\uff0c\u6bd4\u5982\uff1a<\/p>\n<p>ShapeNet\u6570\u636e\u96c6\uff1a\u5305\u542b\u4e86\u7ea6300\u591a\u4e07\u4e2a3D\u6a21\u578b\uff083000\u591a\u7c7b\u7269\u4f53\uff09\uff0c\u6bcf\u4e2a\u6a21\u578b\u6709\u8bed\u4e49\u6ce8\u91ca\u3002\u8fd9\u662f\u5f53\u524d\u6700\u5927\u7684\u4e00\u4e2a\u4e09\u7ef4\u6a21\u578b\u6570\u636e\u96c6\uff1b\u5176\u5b50\u96c6ShapeNetCore\u5177\u6709\u4e00\u4e9b\u624b\u5de5\u7684\u6807\u6ce8\uff1b<\/p>\n<p>ModelNet\u6570\u636e\u96c6\uff1a\u5305\u542b\u4e8612\u591a\u4e2a3D\u6a21\u578b\uff08662\u7c7b\uff09\uff0c\u5305\u542b\u4e24\u4e2a\u5b50\u96c6Model10\u548cModelNet40\uff1b<\/p>\n<p>ShapeGoogle\u6570\u636e\u96c6\uff1a\u5305\u542b\u4e86\u8fd1600\u4e2a\u975e\u521a\u60273D\u6a21\u578b\uff0c\u7528\u4e8e\u68c0\u7d22\u6d4b\u8bd5\uff1b<\/p>\n<p>SHREC\u6570\u636e\u96c6\uff1a\u5305\u542b\u4e86\u4e0a\u5343\u4e2a\u975e\u521a\u60273D\u6a21\u578b\uff0c\u5305\u62ec\u4e0d\u5c11\u4eba\u7684\u6a21\u578b\u548c\u5408\u6210\u6570\u636e\u96c6\uff1b<\/p>\n<p>Watch-N-Patch\u6570\u636e\u96c6\uff1a\u7531Cornell\u5927\u5b66\u548cStanford\u5927\u5b66\u516c\u5e03\uff0c\u4e3b\u8981\u662f\u4eba\u4f533D\u6a21\u578b\u6570\u636e\u3002<\/p>\n<p>\u8fd8\u6709\u4e00\u4e9b\u9ad8\u6821\u548c\u7814\u7a76\u673a\u6784\u516c\u5f00\u4e86\u4e00\u4e9bRGB-D\u6570\u636e\u96c6\uff0c\u5305\u62ecPrinceton\u5927\u5b66\uff08415\u4e2a\u5ba4\u5185\u573a\u666f\uff0c990\u4e07\u4e2a\u6807\u8bb0\u56fe\u50cf\uff09\uff0c\u7ebd\u7ea6\u5927\u5b66\uff08464\u4e2a\u5ba4\u5185\u573a\u666f\uff09\uff0cCornell\u5927\u5b66\uff0824\u4e2a\u529e\u516c\u5ba4\u573a\u666f\uff0c28\u4e2a\u5c45\u5bb6\u5ba4\u5185\u573a\u666f\uff09\uff0cWashington\u5927\u5b66\uff0814\u4e2a\u5ba4\u5185\u573a\u666f\uff09\u7b49\u3002<\/p>\n<p>\u53e6\u5916\uff0c\u745e\u58eb\u82cf\u9ece\u4e16\u5927\u5b66\u53d1\u5e03\u4e86\u4e00\u4e2a\u4f7f\u7528LiDAR\uff08\u6fc0\u51493D\u626b\u63cf\uff09\u626b\u63cf\u768440\u4e2a\u529e\u516c\u5ba4\u573a\u666f\u7684\u9ad8\u7cbe\u5ea63D\u573a\u666f\u6a21\u578b\u6570\u636e\u96c6\u3002<\/p>\n<p>11.3.    3D\u5f62\u72b6\u63cf\u8ff0\u5b50<\/p>\n<p>\u7c7b\u4f3c\u4e8e2D\u56fe\u50cf\uff0c\u4eba\u4eec\u4e5f\u9700\u8981\u5bf93D\u6a21\u578b\u6570\u636e\u8fdb\u884c\u5206\u7c7b\u4e0e\u8bc6\u522b\u3001\u5206\u5272\u4e0e\u5efa\u6a21\u3001\u5339\u914d\u4e0e\u68c0\u7d22\u7b49\u3002\u5b8c\u6210\u8fd9\u4e9b\u4efb\u52a1\u7684\u5173\u952e\u5c31\u662f\u5982\u4f55\u5b9a\u4e49\u548c\u8ba1\u7b973D\u6a21\u578b\u7684\u5f62\u72b6\u63cf\u8ff0\u5b50\uff08Shape descriptors\uff09\u6216\u7279\u5f81\uff08Features\uff09\u3002<\/p>\n<p>\u81f3\u4eca\uff0c\u4eba\u4eec\u5df2\u63d0\u51fa\u4e86\u5404\u79cd\u57fa\u4e8e\u5168\u5c40\u548c\u5c40\u90e8\u7684\u5f62\u72b6\u51e0\u4f55\u5c5e\u6027\u7684\u7a7a\u95f4\u5206\u5e03\u6216\u7edf\u8ba1\u4fe1\u606f\u76843D\u5f62\u72b6\u63cf\u8ff0\u5b50\uff08\u5982\u56fe32\u6240\u793a\uff09\u3002\u8fd9\u4e9b\u5f62\u72b6\u63cf\u8ff0\u5b50\u90fd\u662f\u9488\u5bf9\u67d0\u79cd\u7279\u5b9a\u7684\u5e94\u7528\u6216\u67d0\u4e9b\u7279\u5b9a\u76843D\u6a21\u578b\u7c7b\u578b\u800c\u63d0\u51fa\u7684\uff0c\u540c\u65f6\u6ee1\u8db3\u6240\u6709\u5e94\u7528\u53ca\u6240\u6709\u6a21\u578b\u7c7b\u578b\u76843D\u5f62\u72b6\u63cf\u8ff0\u5b50\u8fd8\u6ca1\u6709\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5e94\u6839\u636e\u7269\u4f53\u7c7b\u578b\u548c\u5177\u4f53\u5e94\u7528\u6765\u9009\u62e9\u5408\u9002\u7684\u5f62\u72b6\u63cf\u8ff0\u5b50\uff08\u7279\u5f81\u9009\u62e9\uff09\u3002\u6bd4\u5982\uff0c\u7b14\u8005\u5982\u4e0b\u8bba\u6587\u4f7f\u7528\u7a00\u758f\u9009\u62e9\u7684\u65b9\u6cd5\u6765\u9009\u62e9\u5408\u9002\u7684\u5f62\u72b6\u63cf\u8ff0\u5b50\u7528\u4e8e3D \u5f62\u72b6\u5206\u5272\u3002<\/p>\n<p>[11-1] Ruizhen Hu, Lubin Fan, Ligang Liu. Co-Segmentation of 3D Shapes via Subspace Clustering. Computer Graphics Forum (Proc. Symposium on Geometry Processing), 31(5): 1703-1713, 2012.<\/p>\n<p>11.4.    3D\u51e0\u4f55\u6570\u636e\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u6311\u6218<\/p>\n<p>\u968f\u77403D\u6570\u636e\uff08\u5305\u62ec\u5355\u4e2a\u6a21\u578b\u4ee5\u53ca\u573a\u666f\u6a21\u578b\uff09\u7684\u65e5\u76ca\u6d41\u884c\u548c\u4e30\u5bcc\uff0c\u5982\u4f55\u5229\u7528\u4e0a\u8ff0\u4e30\u5bcc\u76843D\u6570\u636e\u96c6\u6765\u5b8c\u6210\u5206\u6790\u548c\u5904\u74063D\u5f62\u72b6\u6570\u636e\uff0c\u5df2\u6210\u4e3a\u7814\u7a76\u5de5\u4f5c\u8005\u53ca\u4ea7\u4e1a\u5de5\u4f5c\u8005\u7684\u5173\u6ce8\u7126\u70b9\u548c\u7814\u7a76\u70ed\u70b9\u3002\u56e0\u6b64\uff0c3D\u5f62\u72b6\u7684\u7279\u5f81\u63d0\u53d6\u65b9\u6cd5\u4e5f\u9010\u6b65\u4ece\u4e0a\u8ff0\u7684\u4eba\u5de5\u5b9a\u4e49\u7279\u5f81\u65b9\u6cd5\u5230\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684\u7279\u5f81\u5b66\u4e60\u65b9\u6cd5\u7684\u53d1\u5c55\u3002<\/p>\n<p>\u76f8\u5bf9\u4e8e\u56fe\u50cf\u4e0e\u89c6\u9891\u5904\u7406\uff0c3D\u51e0\u4f55\u6570\u636e\u7684\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u5728\u8fd1\u51e0\u5e74\u624d\u5f00\u59cb\u6709\u4e86\u4e00\u4e9b\u5de5\u4f5c\u548c\u8fdb\u5c55\uff0c\u4f46\u4ecd\u9762\u4e34\u7740\u4e00\u4e9b\u6311\u6218\u3002<\/p>\n<p>(1)  3D\u6570\u636e\u96c6\u8f83\u5c0f<\/p>\n<p>\u76f8\u6bd4\u4e8eImageNet\u7b49\u5343\u4e07\u7ea7\u6570\u636e\u91cf\u76842D\u56fe\u50cf\u6570\u636e\u96c6\uff0c\u73b0\u5728\u76843D\u6a21\u578b\u6570\u636e\u96c6\u7684\u6570\u91cf\u5f88\u5c11\uff0c\u4ecd\u672a\u8fbe\u5230\u201c\u5927\u6570\u636e\u201d\u7684\u89c4\u6a21\u3002\u53e6\u5916\uff0c3D\u6570\u636e\u7684\u6807\u6ce8\u4e5f\u662f\u8f83\u4e3a\u56f0\u96be\u7684\u3002<\/p>\n<p>(2)  3D\u6570\u636e\u662f\u975e\u7ed3\u6784\u5316\u7684<\/p>\n<p>\u56fe\u50cf\u548c\u89c6\u9891\u90fd\u662f\u7ed3\u6784\u5316\u6570\u636e\uff0c\u662f\u7ebf\u6027\u7ed3\u6784\u7684\uff0c\u53ef\u4ee5\u8868\u8fbe\u4e3a\u4e00\u4e2a\u5411\u91cf\u6216\u77e9\u9635\u3002\u4f463D\u6a21\u578b\u6570\u636e\u662f\u975e\u7ed3\u6784\u5316\u7684\uff08\u5982\u56fe33\u6240\u793a\uff09\uff0c\u6bcf\u4e2a\u9876\u70b9\u7684\u90bb\u57df\u6570\u662f\u975e\u56fa\u5b9a\u7684\uff0c\u4ece\u62d3\u6251\u4e0a\u770b\u662f\u4e00\u4e2a\u56fe\uff08Graph\uff09\uff0c\u65e0\u6cd5\u76f4\u63a5\u4f7f\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n<p>(3)  3D\u6570\u636e\u7684\u590d\u6742\u6027<\/p>\n<p>\u76f8\u5bf9\u4e8e\u56fe\u50cf\u548c\u89c6\u9891\uff0c3D\u6a21\u578b\u8fd8\u6709\u5176\u4ed6\u4e00\u4e9b\u590d\u6742\u6027\uff0c\u5305\u62ec\uff1a<\/p>\n<p>(a) \u6b63\u5411\u59ff\u6001\u6027\uff1a\u56fe\u50cf\u57fa\u672c\u90fd\u662f\u6b63\u5411\u62cd\u6444\u7684\uff0c\u4f46\u662f3D\u6a21\u578b\u7684\u59ff\u6001\u53ef\u4ee5\u662f\u4efb\u610f\u7684\uff0c\u5982\u4f55\u6d88\u9664\u59ff\u6001\u7684\u5f71\u54cd\u4ecd\u6709\u6311\u6218\u3002\u4e3a\u4e86\u65b9\u4fbf\uff0c\u4e00\u822c\u4f1a\u9884\u5148\u5c06\u6570\u636e\u96c6\u4e2d\u7684\u6a21\u578b\u7edf\u4e00\u6b63\u671d\u5411\uff1b<\/p>\n<p>(b) \u8868\u8fbe\u4e0d\u7edf\u4e00\uff1a\u56fe\u50cf\u5c31\u662f\u4e00\u4e2a\u77e9\u9635\u7ed3\u6784\uff0c\u8868\u8fbe\u975e\u5e38\u7edf\u4e00\uff1b\u4f46\u662f3D\u6a21\u578b\u6709\u4e0d\u540c\u7684\u8868\u8fbe\u65b9\u5f0f\uff0c\u6bd4\u5982\u70b9\u4e91\u3001\u7f51\u683c\u3001\u4f53\u7d20\u3001\u9690\u51fd\u6570\u3001CSG\u6811\u7b49\uff08\u5982\u56fe34\uff09\uff0c\u4f7f\u5f97\u9700\u8981\u5bf9\u4e0d\u540c\u8868\u8fbe\u7684\u6570\u636e\u8fdb\u884c\u4e0d\u540c\u7684\u5904\u7406\uff1b<\/p>\n<p>(c) \u6570\u636e\u4e0d\u5b8c\u6574\uff1a\u7531\u4e8e\u91c7\u96c6\u8bbe\u5907\u7684\u7cbe\u5ea6\u95ee\u9898\uff0c\u6709\u4e9b3D\u6570\u636e\uff08\u6bd4\u5982RGBD\u6570\u636e\uff09\u4e2d\u5b58\u5728\u7740\u5927\u91cf\u7684\u566a\u58f0\u548c\u6e38\u79bb\u70b9\uff1b\u7531\u4e8e\u906e\u6321\u5173\u7cfb\uff0c\u6709\u4e9b3D\u6570\u636e\u4e0d\u591f\u5b8c\u5168\uff0c\u5b58\u5728\u7740\u7a7a\u6d1e\uff1b\u8fd8\u6709\u4e9b3D\u6570\u636e\u7684\u91c7\u6837\u5bc6\u5ea6\u4e0d\u5747\u5300\uff0c\u9020\u6210\u4e0d\u540c\u90e8\u4f4d\u7684\u4fe1\u606f\u4e0d\u5bf9\u79f0\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image177.jpg\" alt=\"img\" \/><\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image178.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe32. \u5404\u79cd\u4eba\u5de53D\u5f62\u72b6\u63cf\u8ff0\u5b50\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image179.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe33. \u4e8c\u7ef4\u56fe\u50cf\u4e0e\u4e09\u7ef4\u7f51\u683c\u7684\u6570\u636e\u7ed3\u6784\u7684\u533a\u522b\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image180.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe34. \u4e09\u7ef4\u51e0\u4f55\u6570\u636e\u7684\u4e0d\u540c\u8868\u8fbe\u3002<\/p>\n<h2><strong>\u5341\u4e8c\u3001<\/strong>    <strong>\u667a\u80fd\u56fe\u5f62\u5904\u7406\uff1a\u4e09\u7ef4\u6570\u636e\u7684\u6df1\u5ea6\u5b66\u4e60<\/strong><\/h2>\n<p>3D\u56fe\u5f62\u4f5c\u4e3a\u4e00\u79cd\u65b0\u578b\u7684\u53ef\u89c6\u5a92\u4f53\u6570\u636e\u7c7b\u578b\uff0c\u540c\u6837\u53ef\u4ee5\u5229\u7528\u4eba\u5de5\u667a\u80fd\u548c\u6df1\u5ea6\u5b66\u4e60\u7684\u65b9\u6cd5\u6765\u8fdb\u884c\u5206\u6790\u548c\u5904\u7406\uff0c\u878d\u5408\u5927\u6570\u636e\u3001\u5e76\u884c\u8ba1\u7b97\u53ca\u4eba\u5de5\u667a\u80fd\u6280\u672f\u7684\u6700\u65b0\u8fdb\u5c55\u4ee5\u63d0\u9ad8\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u7b97\u6cd5\u53ca\u7cfb\u7edf\u6613\u7528\u6027\u53ca\u6548\u7387\uff0c\u79f0\u4e3a\u667a\u80fd\u56fe\u5f62\u5904\u7406\u3002<\/p>\n<p>\u8fd1\u51e0\u5e74\uff0c\u5df2\u6709\u8d8a\u6765\u8d8a\u591a\u7684\u7814\u7a76\u5de5\u4f5c\u5c06\u673a\u5668\u5b66\u4e60\u548c\u6df1\u5ea6\u5b66\u4e60\u7684\u65b9\u6cd5\u5e94\u7528\u4e8e3D\u6570\u636e\u3002\u672c\u8282\u4ec5\u5c313D\u5f62\u72b6\u63cf\u8ff0\u5b50\u65b9\u9762\u505a\u4e00\u4e2a\u7b80\u7565\u7684\u4ecb\u7ecd\u3002<\/p>\n<p>\u5e94\u7528\u6df1\u5ea6\u5b66\u4e60\u6765\u81ea\u52a8\u62bd\u53d63D\u5f62\u72b6\u7279\u5f81\u4e3b\u8981\u6709\u4ee5\u4e0b3\u79cd\u65b9\u6cd5\uff1a\u7b2c\u4e00\u79cd\uff0c\u57fa\u4e8e\u4f20\u7edf\u7684\u4eba\u5de5\u7279\u5f81\uff08\u7ef4\u6570\u4e00\u81f4\u4e86\uff09\u6765\u8fdb\u884c\u66f4\u62bd\u8c61\u7684\u5f62\u72b6\u7279\u5f81\u7684\u5b66\u4e60\u548c\u62bd\u53d6\uff1b\u8fd9\u79cd\u65b9\u6cd5\u662f\u975e\u7aef\u5230\u7aef\u7684\uff1b\u7b2c\u4e8c\u79cd\uff0c\u5c063D\u6570\u636e\u8f6c\u5316\u4e3a\u89c4\u6574\u7ed3\u6784\u6570\u636e\uff08\u6b27\u6c0f\u533a\u57df\uff09\uff0c\u7136\u540e\u518d\u5e94\u7528\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u62bd\u53d6\u5f62\u72b6\u7279\u5f81\uff0c\u79f0\u4e3a\u663e\u5f0f\u65b9\u6cd5\uff1b\u7b2c\u4e09\u79cd\uff0c\u5c06\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u6539\u9020\u6210\u80fd\u591f\u5904\u7406\u975e\u6b27\u6c0f\u533a\u57df\u6570\u636e\uff0c\u79f0\u4e3a\u9690\u5f0f\u65b9\u6cd5\u3002\u4e0b\u9762\u5206\u522b\u4ece\u65b9\u6cd5\u8bba\u4e0a\u8fdb\u884c\u7b80\u5355\u4ecb\u7ecd\u3002<\/p>\n<p>12.1.    \u57fa\u4e8e\u4eba\u5de5\u7279\u5f81\u7684\u7279\u5f81\u5b66\u4e60\u65b9\u6cd5<\/p>\n<p>\u7531\u4e8e\u4f20\u7edf\u5377\u79ef\u65e0\u6cd5\u76f4\u63a5\u4f5c\u7528\u4e8e3D\u5f62\u72b6\uff0c\u65e9\u671f\u7684\u65b9\u6cd5\u907f\u5f00\u4e86\u76f4\u63a5\u4ee53D\u5f62\u72b6\u4f5c\u4e3a\u8f93\u5165\u7684\u8bad\u7ec3\uff0c\u800c\u662f\u5148\u4ece3D\u6a21\u578b\u4e2d\u63d0\u53d6\u4e00\u4e9b\u4eba\u5de5\u7279\u5f81\uff08\u79f0\u4e3a\u4f4e\u7ea7\u7279\u5f81\uff0c\u5982\u56fe32\uff09\uff0c\u518d\u628a\u8fd9\u4e9b\u7279\u5f81\u8f93\u5165\u5230\u795e\u7ecf\u7f51\u7edc\u4e2d\u8fdb\u884c\u5b66\u4e60\uff0c\u83b7\u5f97\u65b0\u7684\u62bd\u8c61\u7279\u5f81\uff08\u79f0\u4e3a\u9ad8\u7ea7\u7279\u5f81\uff09\uff0c\u5982\u56fe35\u6240\u793a\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image181.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe35. \u57fa\u4e8e\u4eba\u5de5\u7279\u5f81\u7684\u7279\u5f81\u5b66\u4e60\u65b9\u6cd5\u3002<\/p>\n<p>[12-1] Zhige Xie, Kai Xu, Ligang Liu, Yueshan Xiong. 3D Shape Segmentation and Labeling via Extreme Learning Machine. Computer Graphics Forum (Proc. SGP), 33(5): 85-95, 2014.<\/p>\n<p>[12-2] Kan Guo, Dongqing Zou, and Xiaowu Chen. 3D mesh labeling via deep convolutional neural networks. ACM Transactions on Graphics, 35, 1, 2015.<\/p>\n<p>[12-3] Zhenyu Shu, Chengwu Qi, Shiqing Xin, Chao Hu, Li Wang, Yu Zhang, Ligang Liu. Unsupervised 3D Shape Segmentation and Co-segmentation via Deep Learning. Computer Aided Geometric Design (Proc. GMP), 43: 39-52, 2016.<\/p>\n<p>\u4eba\u5de5\u5b9a\u4e49\u7684\u7279\u5f81\u5f88\u5927\u7a0b\u5ea6\u4e0a\u53d6\u51b3\u4e8e\u4eba\u7684\u7ecf\u9a8c\u3002\u56e0\u6b64\uff0c\u57fa\u4e8e\u4eba\u5de5\u7279\u5f81\u7684\u7279\u5f81\u5b66\u4e60\u65b9\u6cd5\u5e76\u4e0d\u662f\u7aef\u5230\u7aef\u7684\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u3002\u53e6\u5916\uff0c\u5404\u79cd\u4eba\u5de5\u7279\u5f81\u5411\u91cf\u7684\u6392\u5217\u4e5f\u4f1a\u6539\u53d8\u7279\u5f81\u77e9\u9635\u53ca\u5176\u5377\u79ef\u540e\u7684\u7ed3\u679c\uff0c\u5bf9\u7ed3\u679c\u4ea7\u751f\u5982\u4f55\u7684\u5f71\u54cd\u4e5f\u4e0d\u6e05\u695a\u3002<\/p>\n<p>12.2.    \u975e\u672c\u5f81\u65b9\u6cd5<\/p>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u662f\u5c063D\u6570\u636e\u8fdb\u884c\u5408\u9002\u7684\u53d8\u6362\uff0c\u5c06\u5176\u53d8\u6362\u5230\u4e00\u4e2a\u6b27\u6c0f\u7a7a\u95f4\u7684\u89c4\u5219\u533a\u57df\uff0c\u4ee5\u4fbf\u9002\u7528\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3002\u6b64\u7c7b\u65b9\u6cd5\u6539\u53d8\u4e863D\u7f51\u683c\u6a21\u578b\u7684\u5f62\u6001\uff0c\u672c\u8d28\u4e0a\u4e5f\u6539\u53d8\u4e86\u6570\u636e\u5206\u5e03\u7a7a\u95f4\uff0c\u662f\u4e3a\u4e86\u9002\u5e94\u4f20\u7edfCNN\u6216MLP\u5bf9\u62d3\u6251\u7684\u8981\u6c42\u800c\u63d0\u51fa\u7684\u6298\u8877\u89e3\u51b3\u65b9\u6cd5\uff0c\u56e0\u6b64\u6210\u4e3a\u57fa\u4e8e\u6b27\u6c0f\u7a7a\u95f4\u7684\u5b66\u4e60\u65b9\u6cd5\u6216\u975e\u672c\u5f81\u65b9\u6cd5\uff0c\u5982\u56fe36\u6240\u793a\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image182.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe36. \u975e\u672c\u5f81\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u3002<\/p>\n<p>\u53d8\u6362\u7684\u533a\u57df\u548c\u65b9\u6cd5\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u79cd\u3002<\/p>\n<p>(1)  \u56fe\u50cf\u533a\u57df\u3002\u6700\u7b80\u5355\u7684\u65b9\u6cd5\u5c31\u662f\u5c063D\u6a21\u578b\u6570\u636e\u6295\u5f71\u5230\u5e73\u9762\u5f62\u6210\u56fe\u50cf\u3002<\/p>\n<p>(a)  \u591a\u89c6\u56fe\u56fe\u50cf\uff1a\u5c063D\u6a21\u578b\u5f80\u591a\u4e2a\u89c6\u89d2\u65b9\u5411\u6295\u5f71\u751f\u6210\u591a\u5e45\u56fe\u50cf\uff0c\u6bd4\u5982[12-4, 12-5]\uff1b<\/p>\n<p>(b)  \u5168\u666f\u56fe\u50cf\uff1a\u5c063D\u6a21\u578b\u5f80\u5e73\u9762\u6295\u5f71\u751f\u6210\u4e00\u5e45\u5168\u666f\u56fe\uff0c\u6bd4\u5982[12-6]\uff1b<\/p>\n<p>(c)  \u53c2\u6570\u5316\u56fe\u50cf\uff1a\u5c063D\u6a21\u578b\u76842D\u53c2\u6570\u5316\u770b\u6210\u4e3a\u4e00\u5e45\u56fe\u50cf\uff0c\u6bd4\u5982[12-7, 12-8]\u3002<\/p>\n<p>(2)  \u4f53\u7d20\u533a\u57df\u3002<\/p>\n<p>(a)  \u7c7b\u6bd4\u4e8e\u56fe\u50cf\u4e2d\u7684\u50cf\u7d20\uff0c\u5c063D\u5f62\u72b6\u770b\u4f5c\u4e09\u7ef4\u4f53\u7d20\u7f51\u683c\u76840\uff0c1\u5206\u5e03\uff0c\u6bd4\u5982[12-9, 12-10\uff0c 12-11]\u3002\u7531\u4e8e\u4f53\u7d20\u7684\u4e2a\u6570\u662f\u4e09\u6b21\u65b9\u589e\u957f\uff0c\u56e0\u6b64\uff0c\u4f53\u7d20\u7684\u5206\u8fa8\u7387\u65e0\u6cd5\u592a\u5927\uff0c\u4e00\u822c\u8fde128x128x128\u7684\u5206\u8fa8\u7387\u505a\u8d77\u6765\u90fd\u5f88\u56f0\u96be\u3002<\/p>\n<p>(b)  \u53ea\u5c06\u6a21\u578b\u8868\u9762\u7528\u4f53\u7d20\u6765\u8868\u8fbe\uff0c\u800c\u7701\u53bb\u5185\u90e8\u4f53\u7d20\u7684\u5b58\u50a8\uff0c\u5e76\u4e14\u5229\u7528\u516b\u53c9\u6811\u7684\u5f62\u5f0f\u6765\u5b58\u50a8\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u63d0\u9ad8\u4f53\u7d20\u7684\u5206\u8fa8\u7387\u53ca\u6a21\u578b\u7684\u8868\u8fbe\u7cbe\u5ea6\uff0c\u6bd4\u5982[12-12]\u3002<\/p>\n<p>(3)  \u57fa\u5143\u7ec4\u5408\u3002\u4e09\u7ef4\u5f62\u72b6\u8fd8\u53ef\u4ee5\u8868\u793a\u6210\u4e00\u4e9b\u57fa\u672c\u5355\u5143\u7684\u7ec4\u5408\uff0c\u5982\u77e9\u5f62\u5757\u3001\u5706\u67f1\u3001\u5706\u9525\u3001\u7403\u7b49\uff0c\u7136\u540e\u5229\u7528\u7f51\u7edc\u6765\u5b66\u4e60\u8fd9\u4e9b\u57fa\u672c\u4f53\u5757\u7684\u53c2\u6570\uff0c\u6bd4\u5982[12-13, 12-14]\u3002<\/p>\n<p>(4)  \u70b9\u4e91\u3002\u76f4\u63a5\u5c063D\u6570\u636e\u770b\u6210\u70b9\u7684\u96c6\u5408\u3002\u5c06\u6bcf\u4e2a\u70b9\u770b\u4f5c\u4e00\u4e2a\u795e\u7ecf\u5143\u8282\u70b9\uff0c\u8282\u70b9\u5305\u542b\u70b9\u7684\u5750\u6807\u6216\u6cd5\u5411\u7b49\u4fe1\u606f\uff0c\u7136\u540e\u5229\u7528\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u63d0\u53d6\u70b9\u7684\u7279\u5f81\u3002\u8fd9\u91cc\u8981\u514b\u670d\u70b9\u53ca\u70b9\u90bb\u57df\u7684\u987a\u5e8f\u65e0\u5173\u6027\u7b49\u3002\u6bd4\u5982[12-14, 12-15, 12-16, 12-18]\u3002<\/p>\n<p>[12-4] Su, H. and S. Maji, et al. (2015). Multi-view convolutional neural networks for 3D shape recognition. ICCV.<\/p>\n<p>[12-5] Xie, Z. and K. Xu, et al. (2015). Projective Feature Learning for 3D Shapes with Multi\u2010View Depth Images. CGF.<\/p>\n<p>[12-6] Shi, B. and S. Bai, et al. (2015). Deeppano: Deep panoramic representation for 3\u2010D shape recognition. IEEE Signal Processing Letters.<\/p>\n<p>[12-7] Sinha, A., Bai, J., Ramani, K., et al. (2016). Deep learning 3D shape surfaces using geometry images. ECCV.<\/p>\n<p>[12-8] Maron, H. and Galun, M. (2017). Convolutional Neural Networks on Surfaces via Seamless Toric Covers. SIGGRAPH.<\/p>\n<p>[12-9] Qi, C. R. and H. Su, et al. (2016). Volumetric and multi-view cnns for object classification on 3D data. CVPR.<\/p>\n<p>[12-10] Brock, A. and T. Lim, et al. (2016). Generative and discriminative voxel modeling with convolutional neural networks. NIPS.<\/p>\n<p>[12-11] Wu, Z., and Song, S. et al. (2015). 3d shapenets: a deep representation for volumetric shapes. CVPR.<\/p>\n<p>[12-12] Wang, P. S. and Liu, Y. et al. (2017). O-cnn: octree-based convolutional neural networks for 3d shape analysis. TOG.<\/p>\n<p>[12-13] J. Li, K. Xu, et al. Grass: Generative recrusive autoencoders for shape structures. ACM Trans. on Graph., 36(4), 2017.<\/p>\n<p>[12-14] S. Tulsiani et al. Learning shape abstraction by assembling volumetric primitives. CVPR, 2017.<\/p>\n<p>[12-15] Garcia-Garcia, A. and Gomez-Donoso, F. et al. (2016). PointNet: A 3D Convolutional Neural Network for real-time object class recognition. IJCNN.<\/p>\n<p>[12-16] Qi, C. R. and H. Su, et al. (2017). PointNet: Deep learning on point sets for 3D classification and segmentation. CVPR.<\/p>\n<p>[12-17] Qi, C. R. and Yi, L. et al. (2017). PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space. CVPR.<\/p>\n<p>[12-18] Yangyan Li, Rui Bu, Mingchao Sun, and Baoquan Chen (2018). PointCNN. arXiv:1801.07791.<\/p>\n<p>12.3.    \u672c\u5f81\u65b9\u6cd5<\/p>\n<p>\u672c\u5f81\u65b9\u6cd5\u76f4\u63a5\u5c06\u4e09\u7ef4\u5f62\u72b6\u770b\u6210\u4e8c\u7ef4\u6d41\u5f62\uff08Manifold\uff09\u6216\u7531\u70b9\u7ec4\u6210\u7684\u56fe\uff08Graph\uff09\uff0c\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e0d\u518d\u662f\u6b27\u6c0f\u8ddd\u79bb\uff0c\u7136\u540e\u76f4\u63a5\u5c06\u5377\u79ef\u5b9a\u4e49\u5728\u8fd9\u6837\u7684\u6570\u636e\u7ed3\u6784\u4e0a\uff0c\u79f0\u4e3a\u975e\u6b27\u6c0f\u7a7a\u95f4\u5b66\u4e60\u7684\u65b9\u6cd5\u6216\u672c\u5f81\u65b9\u6cd5\uff0c\u5982\u56fe37\u3002\u4e24\u79cd\u5178\u578b\u7684\u7f51\u7edc\u4e3a\u6d4b\u5730\u5377\u79ef\u7f51\u7edc\uff08Geodesic CNN, GCNN\uff09\u548c\u56fe\u5377\u79ef\u7f51\u7edc\uff08Graph-based CNN\uff09\uff0c\u5982\u56fe38\uff0c\u53ef\u53c2\u8003[12-19, 12-20, 12-21, 12-22]\u3002<\/p>\n<p>[12-19] Masci, J. and Boscaini, D. et al. (2015). Geodesic convolutional neural networks on Riemannian manifolds. ICCV.<\/p>\n<p>[12-20] Monti, F. and Boscaini, D., Masci. (2016). Geometric deep learning on graphs and manifolds using mixture model CNNs. arXiv preprint arXiv:1611.08402.<\/p>\n<p>[12-21] Boscaini, D. and Masci, J. et al. (2016). Learning shape correspondence with anisotropic convolutional neural networks. NIPS.<\/p>\n<p>[12-22] Yi, L. and Su, H. et al. (2017). Syncspeccnn: Synchronized spectral CNN for 3d shape segmentation. CVPR.<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image183.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe37. \u672c\u5f81\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u3002<\/p>\n<p><img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image184.jpg\" alt=\"img\" \/>  <img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image185.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe38. \u672c\u5f81\u6df1\u5ea6\u5b66\u4e60\u7684\u5177\u4f53\u65b9\u6cd5\u3002\u5de6\uff1a\u6d4b\u5730\u5377\u79ef\uff1b\u53f3\uff1a\u56fe\u5377\u79ef\u7f51\u7edc\u3002<\/p>\n<p>12.4.    \u7aef\u5230\u7aef\u7684\u751f\u6210\u6a21\u578b<\/p>\n<p>\u5728\u4e0a\u9762\u7684\u5de5\u4f5c\u4e2d\uff0c\u6df1\u5ea6\u5b66\u4e60\u7528\u4e8e\u89e3\u51b33D\u5f62\u72b6\u7684\u8bc6\u522b\u3001\u5206\u5272\u3001\u5339\u914d\u548c\u5bf9\u5e94\u7b49\u95ee\u9898\u3002\u8fd1\u5e74\u6765\uff0c\u8d8a\u6765\u8d8a\u591a\u7684\u5de5\u4f5c\u81f4\u529b\u4e8e3D \u6a21\u578b\u7684\u6784\u5efa\u548c\u751f\u6210\uff08\u5927\u90e8\u5206\u90fd\u662f\u4f7f\u7528\u751f\u6210-\u5bf9\u6297\u7f51\u7edcGAN\uff09\u3002\u7531\u4e8e\u53ef\u4ee5\u81ea\u52a8\u751f\u6210\u5927\u91cf\u76843D\u6a21\u578b\uff0c\u5bf9\u4e8e\u6269\u51453D\u6a21\u578b\u6570\u636e\u96c6\u5177\u6709\u91cd\u8981\u7684\u610f\u4e49\uff0c\u975e\u5e38\u503c\u5f97\u5927\u5bb6\u5173\u6ce8\u3002<\/p>\n<p>\u8fd9\u91cc\u7b80\u7565\u4ecb\u7ecd\u4e00\u4e0b\u7aef\u5230\u7aef\u76843D\u6a21\u578b\u751f\u6210\u7684\u4e00\u4e9b\u5de5\u4f5c\u3002\u6240\u8c13\u7aef\u5230\u7aef\u7684\u751f\u6210\u6a21\u578b\uff0c\u5c31\u662f\u8f93\u5165\u662f\u7b80\u5355\u6613\u83b7\u5f97\u7684\uff0c\u8f93\u51fa\u662f\u4e09\u7ef4\u6a21\u578b\uff0c\u4e2d\u95f4\u65e0\u9700\u5176\u4ed6\u64cd\u4f5c\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u4ece\u8f93\u5165\u7684\u4e00\u5f20\u7167\u7247\u8f93\u51fa\u4e09\u7ef4\u4f53\u7d20\u6a21\u578b[12-23, 12-24]\u3001\u70b9\u4e91\u6a21\u578b[12-25]\u3001\u6216\u8005\u7f51\u683c\u6a21\u578b\u53ca\u5176\u53c2\u6570\u5316[12-26]\uff1b[12-27]\u5229\u7528\u7ea7\u8054\u7684\u56fe\u5377\u79ef\u7f51\u7edc\u7531\u7c97\u5230\u7cbe\u9010\u6e10\u7ec6\u5316\u7f51\u683c\u6a21\u578b\uff1b[12-28]\u7531\u624b\u7ed8\u8349\u56fe\u751f\u6210\u53c2\u6570\u5316\u7684\u5938\u5f20\u4eba\u8138\u6a21\u578b\u3002<\/p>\n<p>[12-23] J. Wu et al. Learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling. Advances in Neural Information Processing Systems, 82-90, 2016.<\/p>\n<p>[12-24] J. Li et al. Grass: Generative recursive autoencoders for shape structures. Siggraph 2017.<\/p>\n<p>[12-25] H. Fan et al. A point set generation network for 3D object reconstruction from a single image. CVPR 2017.<\/p>\n<p>[12-26] T. Groueix et al. AltasNet: A papier approach to learning 3D surface generation. arXiv: 1802.05384, 2018.<\/p>\n<p>[12-27] N. Wang et al. Pixel2Mesh: Generating 3D mesh models form single RGB iamges. arXiv: 1804.01654.<\/p>\n<p>[12-28] X. Han et al. DeepSketch2Face: A deep learning based sketching systems for 3D face and caricature modeling. Siggraph 2017.<\/p>\n<h2>\u3010\u540e\u8bb0\u3011<\/h2>\n<p>\u6b64\u6587\u5206\u4eab\u4e86\u7b14\u8005\u5bf9\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u7406\u89e3\uff0c\u4ece\u903c\u8fd1\u8bba\u7684\u89d2\u5ea6\u6df1\u5165\u6d45\u51fa\u5730\u7406\u89e3\u4e86\u6df1\u5ea6\u5b66\u4e60\u7684\u539f\u7406\uff0c\u4e86\u89e3\u4e86\u6574\u4e2a\u8c03\u8bd5\u6df1\u5ea6\u7f51\u7edc\u7684\u201c\u70bc\u4e39\u201d\u8fc7\u7a0b\uff0c\u662f\u4e2a\u9700\u8981\u4e30\u5bcc\u7ecf\u9a8c\u7684\u201c\u6280\u672f\u6d3b\u201d\u3002\u673a\u5668\u5b66\u4e60\u8fd8\u6709\u5f88\u591a\u5176\u4ed6\u91cd\u8981\u7684\u65b9\u6cd5\uff0c\u6bd4\u5982\u975e\u76d1\u7763\u5b66\u4e60\u548c\u5f3a\u5316\u5b66\u4e60\u7b49\uff0c\u7b14\u8005\u5c31\u4e0d\u4e00\u4e00\u8fdb\u884c\u4ecb\u7ecd\u4e86\u3002<\/p>\n<p>\u4ece\u672c\u6587\u7684\u5206\u6790\u53ef\u77e5\uff0c\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u80cc\u540e\u7684\u8fd0\u884c\u539f\u7406\u4e3b\u8981\u57fa\u4e8e\u6570\u636e\u9a71\u52a8\u7684\u51fd\u6570\u62df\u5408\uff0c\u91c7\u7528\u7684\u662f\u201c\u7ecf\u9a8c\u4e3b\u4e49\u201d\u7684\u5b9e\u7528\u65b9\u6cd5\uff08\u6bd4\u5982\u6570\u5b66\u4e2d\u7684\u6700\u5c0f\u4e8c\u4e58\u65b9\u6cd5\u53ca\u7edf\u8ba1\u5b66\u4e2d\u7684\u7edf\u8ba1\u56de\u5f52\u65b9\u6cd5\u7b49\uff09\uff1b\u5b83\u79bb\u771f\u6b63\u7684\u4eba\u5de5\u667a\u80fd\uff0c\u5373\u80fd\u901a\u8fc7\u56fe\u7075\u6d4b\u8bd5\uff08Turing Testing\uff09\u7684\u667a\u80fd\u673a\u5668\u8fd8\u5f88\u8fdc\u3002\u4ece\u6570\u5b66\u672c\u8d28\u4e0a\u6765\u770b\uff0c\u73b0\u5728\u57fa\u4e8e\u6570\u636e\u7684\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u5b9e\u8d28\u4e0a\u53ea\u6709\u201c\u8bb0\u5fc6\u201d\u80fd\u529b\uff0c\u5e76\u6ca1\u6709\u5bf9\u95ee\u9898\u7684\u201c\u7406\u89e3\u201d\u80fd\u529b\uff0c\u66f4\u6ca1\u6709 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src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image186.jpg\" alt=\"img\" \/><\/p>\n<p>\u56fe39. Gartner 2018\u4eba\u5de5\u667a\u80fd\u6280\u672f\u6210\u719f\u5ea6\u66f2\u7ebf\u3002\uff08\u56fe\u7247\u6765\u6e90\u4e8e\u4e92\u8054\u7f51\uff09<\/p>\n<p>\u4e94\u5e74\u524d\uff082013\u5e744\u6708\uff09\uff0c\u300a\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u6280\u672f\u8bc4\u8bba\u300b\u6742\u5fd7\u5c06\u6df1\u5ea6\u5b66\u4e60\u5217\u4e3a2013\u5e74\u5341\u5927\u7a81\u7834\u6027\u6280\u672f\uff08Breakthrough Technology\uff09\u4e4b\u9996\u3002\u7ecf\u8fc7\u524d\u51e0\u5e74\u7684\u9ad8\u901f\u53d1\u5c55\uff0c\u6839\u636eGartner\u57287\u6708\u521a\u53d1\u5e03\u76842018\u4eba\u5de5\u667a\u80fd\u6280\u672f\u6210\u719f\u5ea6\u66f2\u7ebf\uff08\u5982\u56fe39\uff09\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u53ca\u6df1\u5ea6\u5b66\u4e60\u5df2\u4ece\u524d\u51e0\u5e74\u7684\u722c\u5761\u9636\u6bb5\u5230\u8fbe\u9876\u90e8\u3002\u672a\u6765\uff0c\u76f8\u4fe1\u4eba\u4eec\u5c06\u4f1a\u66f4\u51b7\u9759\u5730\u6765\u770b\u5f85\u53ca\u53d1\u5c55\u76f8\u5173\u7684\u6280\u672f\u548c\u5e94\u7528\u3002<\/p>\n<p>\u6700\u8fd1\uff0c\u6709\u4eba\u63d0\u51fa\u201c\u53ef\u5fae\u7f16\u7a0b\uff08Differentiable Programming\uff09\u201d\u7684\u6982\u5ff5\uff0c\u5c31\u662f\u5c06\u795e\u7ecf\u7f51\u7edc\u5f53\u6210\u4e00\u79cd\u8bed\u8a00\uff08\u800c\u4e0d\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\uff09\uff0c\u6765\u63cf\u8ff0\u6211\u4eec\u5ba2\u89c2\u4e16\u754c\u7684\u89c4\u5f8b\u3002\u751a\u81f3Yann LeCun\u66fe\u5728Facebook\u7684\u6587\u7ae0\u4e2d\u8bf4\u9053\uff1a\u201cDeep Learning Is Dead. Long Live Differentiable Programming!\u201d\uff08\u6df1\u5ea6\u5b66\u4e60\u5df2\u6b7b\uff0c\u53ef\u5fae\u7f16\u7a0b\u6c38\u751f\uff09 \u8fd9\u4e2a\u6982\u5ff5\u7684\u63d0\u51fa\u53c8\u5c06\u795e\u7ecf\u7f51\u7edc\u63d0\u9ad8\u4e86\u4e00\u4e2a\u5c42\u6b21\u3002<\/p>\n<p>\u672c\u6587\u5b8c\u7a3f\u6838\u5bf9\u65f6\uff0c\u7b14\u8005\u53d1\u73b0\u6587\u4e2d\u6709\u4e9b\u6570\u5b66\u7b26\u53f7\uff08\u6bd4\u5982<img src=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/DL\/What_is_DeepLearning.files\/image187.png\" alt=\"img\" \/>\u7b49\uff09\u5b58\u5728\u7740\u91cd\u590d\u5b9a\u4e49\u4e0e\u4f7f\u7528\uff0c\u4f46\u6839\u636e\u4e0a\u4e0b\u6587\u5e76\u4e0d\u5f71\u54cd\u9605\u8bfb\u548c\u7406\u89e3\uff0c\u56e0\u6b64\u7b14\u8005\u5c31\u4e0d\u82b1\u65f6\u95f4\u53bb\u4fee\u6b63\u4e86\uff0c\u5728\u6b64\u8bf4\u660e\u4e0b\u3002<\/p>\n<p>\u518d\u6b21\u58f0\u660e\u4e0b\uff0c\u7b14\u8005\u7684\u4e3b\u8981\u7814\u7a76\u9886\u57df\u4e3a<a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\/Resources\/CG\/What_is_CG.htm\">\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66<\/a>\uff0c\u800c\u975e\u4eba\u5de5\u667a\u80fd\u9886\u57df\uff0c\u56e0\u6b64\u672c\u6587\u4ec5\u4ec5\u4e3a\u7b14\u8005\u4ece\u5916\u884c\u7684\u89d2\u5ea6\u5bf9\u57fa\u4e8e\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u7684\u7c97\u6d45\u7406\u89e3\uff0c\u800c\u975e\u4eba\u5de5\u667a\u80fd\u9886\u57df\u5bf9\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u548c\u6df1\u5ea6\u5b66\u4e60\u7684\u6743\u5a01\u89e3\u91ca\u3002\u7b14\u8005\u5bf9\u5176\u4e2d\u7684\u6709\u4e9b\u5185\u5bb9\u7684\u7406\u89e3\u662f\u6709\u9650\u7684\uff0c\u751a\u81f3\u662f\u6709\u8bef\u7684\u3002\u56e0\u6b64\uff0c\u8be5\u6587\u4ec5\u4f9b\u8bfb\u8005\u53c2\u8003\uff0c\u4e0d\u4f5c\u4e3a\u4e13\u4e1a\u8d44\u6599\uff01\u5982\u6709\u4e0d\u5f53\u4e4b\u5904\uff0c\u8fd8\u8bf7\u8bfb\u8005\u6307\u6b63\uff01<\/p>\n<p>\u3010\u81f4\u8c22\u3011<\/p>\n<p>\u7b14\u8005\u5728\u5b66\u4e60\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u53ca\u6df1\u5ea6\u5b66\u4e60\u7684\u8fc7\u7a0b\u4e2d\uff0c\u9605\u8bfb\u4e86\u8bb8\u591a\u76f8\u5173\u7684\u4e66\u7c4d\u548c\u8bba\u6587\uff08\u6bd4\u5982\u5468\u5fd7\u534e\u8001\u5e08\u7684\u300a\u673a\u5668\u5b66\u4e60\u300b\u4e00\u4e66\u548c\u674e\u5b8f\u6bc5\u8001\u5e08\u7684\u8bfe\u4ef6\u7b49\uff09\u4ee5\u53ca\u5fae\u4fe1\u8ba2\u9605\u53f7\uff08\u6bd4\u5982\u300aSigAI\u300b\u3001\u300a\u4eba\u5de5\u667a\u80fd\u5b66\u5bb6\u300b\u3001\u300a\u6df1\u5ea6\u5b66\u4e60\u5927\u8bb2\u5802\u300b\u3001\u300a\u8001\u987e\u8c08\u51e0\u4f55\u300b\u7b49\uff09\uff0c\u5728\u6b64\u8868\u793a\u611f\u8c22\u3002\u4e5f\u611f\u8c22\u8212\u632f\u5b87\u3001\u5f90\u51ef\u3001\u97e9\u6653\u5149\u3001\u6c88\u5c0f\u52c7\u3001\u80e1\u745e\u73cd\u7b49\u540c\u884c\u3001\u4ee5\u53ca\u7b14\u8005\u5b9e\u9a8c\u5ba4\u7684\u540c\u4e8b\uff08\u5f20\u4e3e\u52c7\u3001\u5085\u5b5d\u660e\u3001\u6768\u5468\u65fa\u7b49\uff09\u548c\u5b66\u751f\uff08\u9648\u660e\u4f73\u3001\u65b9\u6e05\u3001\u675c\u51ac\u3001\u77f3\u78ca\u3001\u6b27\u9633\u6587\u6e05\u3001\u5218\u4e2d\u8fdc\u7b49\uff09\uff0c\u4e0e\u4ed6\u4eec\u7684\u4ea4\u6d41\u548c\u8ba8\u8bba\u4e5f\u8ba9\u7b14\u8005\u53d7\u76ca\u532a\u6d45\u3002<\/p>\n<p>\u6700\u540e\uff0c\u5e0c\u671b\u60a8\u80fd\u4ece\u672c\u6587\u53d7\u76ca\u3002\u795d\u60a8\u5065\u5eb7\u3001\u5feb\u4e50\u3001\u6210\u529f\uff01<\/p>\n<p>\u5218\u5229\u521a<\/p>\n<p>\u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\u56fe\u5f62\u4e0e\u51e0\u4f55\u8ba1\u7b97\u5b9e\u9a8c\u5ba4(<a href=\"http:\/\/gcl.ustc.edu.cn\/\">http:\/\/gcl.ustc.edu.cn<\/a>)<\/p>\n<p>\u4e2a\u4eba\u4e3b\u9875\uff1a<a href=\"http:\/\/staff.ustc.edu.cn\/~lgliu\">http:\/\/staff.ustc.edu.cn\/~lgliu<\/a><\/p>\n<p>\u7535\u5b50\u90ae\u7bb1\uff1a<a href=\"mailto:lgliu@ustc.edu.cn\">lgliu@ustc.edu.cn<\/a><\/p>\n<p>2018\u5e748\u67088\u65e5<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5218\u5229\u521a \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\u56fe\u5f62\u4e0e\u51e0\u4f55\u8ba1\u7b97\u5b9e\u9a8c\u5ba4 http:\/\/staff.ustc.edu.cn\/~lgliu \u539f\u6587\u94fe\u63a5\uff1a http:\/\/   \u2026 &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[59],"tags":[60],"_links":{"self":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts\/1054"}],"collection":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1054"}],"version-history":[{"count":2,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/1054\/revisions"}],"predecessor-version":[{"id":1056,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/1054\/revisions\/1056"}],"wp:attachment":[{"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1054"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1054"},{"taxonomy":"post_tag","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1054"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}