{"id":494,"date":"2018-12-13T17:33:36","date_gmt":"2018-12-13T09:33:36","guid":{"rendered":"http:\/\/localhost\/?p=494"},"modified":"2019-01-15T14:49:04","modified_gmt":"2019-01-15T06:49:04","slug":"back-propagation%e7%ae%97%e6%b3%95%e5%8e%9f%e7%90%86%e7%ae%80%e8%bf%b0","status":"publish","type":"post","link":"http:\/\/www.ahomer.cn\/?p=494","title":{"rendered":"back propagation\u7b97\u6cd5\u539f\u7406\u7b80\u8ff0"},"content":{"rendered":"<p>back propagation -  \u5373\u53cd\u5411\u4f20\u64ad\uff0c\u56e0\u4e3aerror function\u662f\u5173\u4e8e\u8f93\u51fa\u5c42\u7684\u51fd\u6570\uff0cerror function\u5bf9\u9690\u85cf\u5c42\u7cfb\u6570\u6c42\u504f\u5bfc\u6d89\u53ca\u8f93\u51fa\u5c42\u6c42\u5bfc\uff0c\u6240\u4ee5\uff0c\u672c\u8d28\u4e0a\uff0c\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684\u63a8\u5bfc\uff0c\u662f\u94fe\u5f0f\u6c42\u5bfc\u7684\u63a8\u5bfc\u8fc7\u7a0b\u3002\u6240\u4ee5\u6211\u4eec\u5148\u770b\u770b\u94fe\u5f0f\u6c42\u5bfc(\u590d\u5408\u6c42\u5bfc)\u3002<\/p>\n<p>\u5047\u8bbe\uff1a<br \/>\nh = f(u) = f(w,x)<br \/>\ny = g(u') = g(w',h)<\/p>\n<p>\u90a3\u4e48\uff1a<br \/>\ndy\/dw' = dg\/du' * du\/dw'<\/p>\n<p>\u5176\u4e2d\uff0c\u6211\u4eec\u5047\u8bbeh\u4e3a\u9690\u85cf\u5c42\uff0cy\u4e3a\u8f93\u51fa\u5c42\uff08\u7b80\u5316\u63cf\u8ff0\uff0c\u5047\u8bbe\u5c311\u4e2a\u8f93\u5165\u5c42\u30011\u4e2a\u9690\u5c42\u30011\u4e2a\u8f93\u51fa\u5c42\uff09<br \/>\n\u5728\u6574\u4e2a\u63a8\u5bfc\u8fc7\u7a0b\uff0c\u6211\u4eec\u7684\u76ee\u7684\u662f\u6c42\u5f97w\u3001w'\uff0c\u5373\u7f51\u7edc\u53c2\u6570\u3002<\/p>\n<p>\u9690\u85cf\u5c42\u7cfb\u6570\uff1aw<br \/>\n\u8f93\u51fa\u5c42\u7cfb\u6570\uff1aw'<\/p>\n<p>\u5047\u8bbe\u6211\u4eec\u91c7\u7528MSE\u4f5c\u4e3aloss function\uff1a<br \/>\nE =  1\/2 *sum( (label - y)^2 )<\/p>\n<p><strong>1\u3001\u8f93\u51fa\u5c42<\/strong><br \/>\n\u8f93\u51fa\u5c42\u7684\u8f93\u5165\u4e3a\u9690\u85cf\u5c42h\u8f93\u51fau'\uff0c\u5bf9\u4efb\u610f\u8f93\u51fa\u5c42\u7684\u8f93\u5165ui'\u8fdb\u884c\u6c42\u5bfc\uff1a<br \/>\ndE\/dui' = dE\/dy * dy\/dui' =  (y-label) * dy\/dui' \u8bb0\u4e3a EI'<br \/>\n\u7531\u4e8ey\u4e00\u822c\u4e3asigmoid function\uff0cy\u4e3a\u8bad\u7ec3\u8fc7\u7a0b\u8f93\u51fa\u503c\uff08\u4f9d\u8d56\u9690\u85cf\u5c42\u3001\u8f93\u5165\u5c42\u7b49\uff09\uff0clabel\u4e3a\u76ee\u6807\u503c<\/p>\n<p>\u6240\u4ee5\uff1a<br \/>\nEI' = (y-label) * y * (1-y)<\/p>\n<p>\u5bf9\u4efb\u610f\u7684\u8f93\u51fa\u5c42\u7684\u7cfb\u6570wi' \u6c42\u5bfc\uff0c\u590d\u5408\u6c42\u5bfc\uff0c\u5148\u6c42y\u7684\u76f8\u5173\u7cfb\u6570h\uff0c\u7136\u540eh\u5173\u4e8ewi'\u6c42\u5bfc<br \/>\ndE\/dwi' = dE\/dui' * dui'\/dwi' = EI' * dui'\/dwi'<\/p>\n<p>\u7531\u4e8e\uff1a<br \/>\nu' = sum(h * w')<br \/>\n\u6240\u4ee5\uff1a<br \/>\ndE\/dwi' = dE\/dui' * dui'\/dwi' = EI' * hi<\/p>\n<p><strong>2\u3001\u9690\u85cf\u5c42<\/strong><br \/>\nh\u4e3a\u9690\u85cf\u5c42\u7684\u8f93\u51fa\uff0c\u53c2\u7167\u4ee5\u4e0a\u6d41\u7a0b\uff0c\u5bf9\u4efb\u610fhi\u6c42\u5bfc\uff0cu'\u662f\u5173\u4e8eh\u7684\u51fd\u6570\uff0c\u6839\u636e\u590d\u5408\u6c42\u5bfc\u89c4\u5219\uff1a<br \/>\ndE\/dhi = dE\/du' * du'\/dhi = EI' * wi'<\/p>\n<p>\u53ef\u4ee5\u770b\u5230\u9690\u85cf\u7684\u6c42\u5bfc\u7ed3\u679c\u4f9d\u8d56\u4e86\u8f93\u51fa\u5c42\u7684\u6c42\u5bfc\u7ed3\u679c\uff0c\u4e5f\u5373\uff0c\u4f53\u73b0\u4e86\u53cd\u5411\u4f20\u64ad\u7684\u5185\u5728\u542b\u4e49\u3002<\/p>\n<p>\u7ee7\u7eed\u5bf9\u9690\u85cf\u5c42\u7684\u4efb\u610f\u7cfb\u6570\u6c42\u5bfc\uff1awi<br \/>\ndE\/dwi =  dE\/dhi * dhi\/dui * dui\/dwi = EI' * wi' * dhi\/dui * xi<\/p>\n<p>dhi\/dui \u53d6\u51b3\u4e8e\u9690\u85cf\u5c42\u91c7\u7528\u4ec0\u4e48\u7c7b\u578b\u7684\u76ee\u6807\u51fd\u6570\uff0c\u5047\u8bbe\u8fd8\u662fsigmod function\uff0c\u5219\uff1a<br \/>\ndE\/dwi = EI' * wi' * hi * (1-hi) * xi \u8bb0\u4e3a EI<\/p>\n<p>\u53ef\u89c1\uff0c\u9690\u85cf\u5c42\u7684\u53c2\u6570\u66f4\u65b0\u4f9d\u8d56\u4e8e \u8f93\u51fa\u5c42\u7684EI'\uff0c\u521d\u59cb\u5316\u968f\u673a\u6492\u70b9\uff0c\u5f97\u5230y\uff0c\u6839\u636e\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u66f4\u65b0wi\u3001wi'\uff0c\u5373\u53ef\u6c42\u5f97wi\u3001wi'\u7cfb\u6570\u3002<\/p>\n<p>\u53c2\u8003\uff1a<a href=\"https:\/\/arxiv.org\/abs\/1411.2738\">arXiv\uff1a1411.2738<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>back propagation &#8211; \u5373\u53cd\u5411\u4f20\u64ad\uff0c\u56e0\u4e3aerror function\u662f\u5173\u4e8e\u8f93\u51fa\u5c42\u7684\u51fd\u6570\uff0cerro [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-494","post","type-post","status-publish","format-standard","hentry","category-program"],"_links":{"self":[{"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=\/wp\/v2\/posts\/494","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=494"}],"version-history":[{"count":9,"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions"}],"predecessor-version":[{"id":507,"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions\/507"}],"wp:attachment":[{"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=494"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.ahomer.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}