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\/>\n\u603b\u7684\u6765\u8bf4\uff0c\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08RNN\uff09\u548c\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff08Feedforward Neural Network\uff09\u662f\u4e24\u79cd\u4e0d\u540c\u7c7b\u578b\u7684\u795e\u7ecf\u7f51\u8def\u3002<\/p>\n<ul>\n<li>\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u662f\u4e00\u79cd\u6700\u7b80\u5355\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u5176\u7279\u70b9\u662f\u4fe1\u606f\u4ece\u8f93\u5165\u5c42\u6d41\u5411\u8f93\u51fa\u5c42\uff0c\u4e0d\u5b58\u5728\u5faa\u73af\u94fe\u63a5\uff0c\u5b83\u9002\u7528\u4e8e\u7b80\u4ecb\u7b80\u5355\u7684\u56de\u5f52\u95ee\u9898\u6216\u8005\u5206\u7c7b\u95ee\u9898\u3002<\/li>\n<li>\u5faa\u73af\u795e\u7ecf\u7f51\u8def\u5219\u5177\u6709\u4e00\u4e2a\u6216\u8005\u591a\u4e2a\u5faa\u73af\u94fe\u63a5\uff0c\u4f7f\u5f97\u5b83\u80fd\u591f\u5904\u7406\u5e8f\u5217\u6570\u636e\uff0c\u4f8b\u5982\u6587\u672c\u3001\u97f3\u9891\u548c\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u3002<\/li>\n<\/ul>\n<p>RNN\u53ef\u4ee5\u5728\u6bcf\u4e00\u6b65\u7684\u8f93\u5165\u4e0a\u8003\u8651\u524d\u9762\u7684\u4fe1\u606f\uff0c\u4ece\u800c\u5bf9\u6bcf\u4e2a\u65f6\u95f4\u6b65\u751f\u6210\u4e00\u4e2a\u8f93\u51fa\u3002\u56e0\u6b64\uff0cRNN\u975e\u5e38\u9002\u7528\u4e8e\u5904\u7406\u5e8f\u5217\u6570\u636e\u548c\u9884\u6d4b\u95ee\u9898\u3002<br \/>\n\u5728\u5e94\u7528\u5c42\u9762\u4e0a\uff0c\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u9002\u7528\u4e8e\u7b80\u5355\u7684\u56de\u5f52\u548c\u5206\u7c7b\u95ee\u9898\uff0c\u800c\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\u9002\u7528\u4e8e\u5904\u7406\u5e8f\u5217\u6570\u636e\u548c\u9884\u6d4b\u95ee\u9898\u3002<\/p>\n<h4>\u4e3a\u4ec0\u4e48\u4e0d\u9002\u7528\u9690\u9a6c\u5c14\u79d1\u592b\u6a21\u578b\u505a\u65f6\u5e8f\u6570\u636e\u7684\u5efa\u6a21<\/h4>\n<p>Markov chain\u80fd\u591f\u5efa\u6a21\u4e00\u4e2a\u89c2\u6d4b\u5e8f\u5217\u5bf9\u5e94\u7684\u72b6\u6001\u8f6c\u79fb\u6982\u7387\u3002Hidden Markov Models\u80fd\u591f\u5efa\u6a21\u4e00\u4e2a\u89c2\u6d4b\u7eed\u8054\u4f5c\u4e3a\u4e00\u4e2a\u6982\u7387\u4f9d\u8d56\u4e8e\u4e00\u4e2a\u65e0\u6cd5\u89c2\u6d4b\u5230\u7684\u72b6\u6001\u5e8f\u5217\u3002\u7136\u800c\uff0c\u4f20\u7edf\u7684Markov model\u662f\u6709\u9650\u5236\u7684\uff0c\u56e0\u4e3a\u4ed6\u4eec\u7684\u72b6\u6001\u5fc5\u987b\u4ece\u4e00\u4e2a\u540c\u7b49\u5927\u5c0f\u7684\u79bb\u6563\u72b6\u6001\u7a7a\u95f4S\u83b7\u5f97\uff0c\u7136\u540e\u4f7f\u7528Viterbi\u7b97\u6cd5\u8fdb\u884c\u89e3\u7801\uff0c\u901a\u8fc7\u8f6c\u79fb\u6765\u6355\u83b7\u4efb\u610f\u4e24\u4e2a\u65f6\u95f4\u72b6\u6001\u7684\u8f6c\u79fb\u6982\u7387\u3002\u4f46\u662f\u5f53\u53ef\u80fd\u7684\u9690\u85cf\u72b6\u6001\u96c6\u6269\u5927\uff0c\u6807\u51c6\u64cd\u4f5c\u5c31\u4f1a\u5931\u6548\u3002\u6bcf\u4e00\u4e2a\u9690\u72b6\u6001\u4ec5\u4ec5\u4f9d\u8d56\u4e8e\u524d\u4e00\u4e2a\u72b6\u6001\uff0c\u6240\u4ee5\u901a\u8fc7\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u72b6\u6001\u7a7a\u95f4\u6765\u6269\u5c55\u4e00\u4e2aMarkov\u6a21\u578b\u6765\u89e3\u91ca\u4e00\u4e2a\u66f4\u5927\u7684\u4e0a\u4e0b\u6587\u7a97\u53e3\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u4f7f\u72b6\u6001\u7a7a\u95f4\u968f\u7a97\u53e3\u7684\u5927\u5c0f\u5448\u6307\u6570\u7ea7\u589e\u957f\u3002\u8fd9\u5c31\u4f7f\u5f97HMM\u5728\u8ba1\u7b97\u4e0a\u4e0d\u5408\u9002\u5bf9\u5177\u6709\u957f\u671f\u4ee5\u6765\u7684\u6570\u636e\u5efa\u6a21\u3002<\/p>\n<p>RNN\u53ef\u4ee5\u6355\u6349\u957f\u671f\u65f6\u95f4\u4f9d\u8d56\u6027\uff0c\u514b\u670d\u4e86\u9a6c\u5c14\u79d1\u592b\u6a21\u578b\u7684\u4e3b\u8981\u5c40\u9650\u6027\u3002\u8fd9\u662f\u56e0\u4e3aRNN\u4e2d\u7684\u4efb\u610f\u72b6\u6001\u53ef\u4ee5\u5305\u542b\u51e0\u4e4e\u4efb\u610f\u957f\u5ea6\u7a97\u53e3\u5185\u7684\u4fe1\u606f\u3002\u5728\u4f20\u7edf\u7684RNN\u4e2d\u4efb\u610f\u72b6\u6001\u90fd\u4ec5\u4f9d\u8d56\u5f53\u524d\u7684\u8f93\u5165\u53ca\u5728\u7f51\u7edc\u4e2d\u524d\u4e00\u4e2a\u65f6\u95f4\u6b65\u7684\u72b6\u6001\uff0c\u56e0\u6b64\uff0c\u5728\u4efb\u610f\u6b65\u7684\u9690\u72b6\u6001\u90fd\u5305\u542b\u4e86\u51e0\u4e4e\u4efb\u610f\u5728\u5f53\u524d\u65f6\u95f4\u6b65\u4e4b\u524d\u7684\u65f6\u95f4\u6b65\u4e2d\u7684\u4fe1\u606f\uff0c\u4e0d\u540c\u7684\u72b6\u6001\u7684\u6570\u636e\u53ef\u4ee5\u8868\u793a\u5728\u4e00\u4e2a\u9690\u85cf\u5c42\u8282\u70b9\u968f\u8282\u70b9\u7684\u6570\u91cf\u5448\u6307\u6570\u6027\u589e\u957f\u3002\u5373\u4f7f\u6bcf\u4e2a\u8282\u70b9\u53ea\u53d6\u4e8c\u8fdb\u5236\uff0c\u8fd9\u4e2a\u7f51\u7edc\u6700\u591a\u4f1a\u5448\u73b0\u51fa2n\u4e2a\u72b6\u6001\uff0c\u5176\u4e2dN\u662f\u9690\u85cf\u5c42\u8282\u70b9\u7684\u4e2a\u6570\u3002<\/p>\n<p>RNN\u76f8\u8f83\u4e8eHMM\u66f4\u597d\u3001\u66f4\u5e7f\u6cdb\u7684\u539f\u56e0\u4e3b\u8981\u5305\u62ec\uff1a<\/p>\n<ul>\n<li>\u8868\u8fbe\u80fd\u529b\uff1aRNN\u5177\u6709\u66f4\u5f3a\u7684\u8868\u8fbe\u80fd\u529b\u3002\u901a\u8fc7\u5faa\u73af\u795e\u7ecf\u5143\u548c\u5171\u4eab\u6743\u91cd\uff0cRNN\u53ef\u4ee5\u5728\u4e0d\u540c\u7684\u65f6\u95f4\u6b65\u957f\u5904\u7406\u4e0d\u540c\u957f\u5ea6\u7684\u5e8f\u5217\u3002\u4e0e\u6b64\u540c\u65f6\uff0cHMM\u5bf9\u6570\u636e\u7684\u5904\u7406\u4e3b\u8981\u57fa\u4e8e\u72b6\u6001\u8f6c\u79fb\u548c\u89c2\u6d4b\u6982\u7387\uff0c\u5176\u8868\u8fbe\u80fd\u529b\u8f83\u5f31\uff0c\u4e0d\u80fd\u5f88\u597d\u5730\u6355\u6349\u590d\u6742\u7684\u65f6\u5e8f\u5173\u7cfb\u3002<\/li>\n<li>\u957f\u8ddd\u79bb\u4f9d\u8d56\uff1aRNN\u53ef\u4ee5\u5b66\u4e60\u6355\u6349\u957f\u8ddd\u79bb\u4f9d\u8d56\u3002\u867d\u7136\u666e\u901aRNN\u5728\u5904\u7406\u957f\u8ddd\u79bb\u4f9d\u8d56\u65f6\u53ef\u80fd\u4f1a\u9047\u5230\u68af\u5ea6\u6d88\u5931\/\u68af\u5ea6\u7206\u70b8\u7684\u95ee\u9898\uff0c\u4f46\u53ef\u4ee5\u901a\u8fc7\u5f15\u5165\u957f\u77ed\u65f6\u8bb0\u5fc6\u7f51\u7edc\uff08LSTM\uff09\u548c\u95e8\u63a7\u5faa\u73af\u5355\u5143\uff08GRU\uff09\u7b49\u7ed3\u6784\u6709\u6548\u5730\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u3002HMM\u5728\u5904\u7406\u957f\u8ddd\u79bb\u4f9d\u8d56\u65f6\u6548\u679c\u8f83\u5dee\u3002<\/li>\n<li>\u7aef\u5230\u7aef\u8bad\u7ec3\uff1aRNN\u53ef\u4ee5\u8fdb\u884c\u7aef\u5230\u7aef\u8bad\u7ec3\uff0c\u5373\u5728\u540c\u4e00\u4e2a\u6a21\u578b\u4e2d\u540c\u65f6\u5b66\u4e60\u7279\u5f81\u8868\u793a\u548c\u4efb\u52a1\u76ee\u6807\u3002\u8fd9\u4f7f\u5f97RNN\u80fd\u591f\u5728\u7279\u5b9a\u4efb\u52a1\u4e0a\u83b7\u5f97\u66f4\u597d\u7684\u6027\u80fd\u3002\u76f8\u53cd\uff0cHMM\u901a\u5e38\u9700\u8981\u624b\u52a8\u8bbe\u8ba1\u7279\u5f81\u548c\u91c7\u7eb3\u6570\uff0c\u5176\u8bad\u7ec3\u8fc7\u7a0b\u6d89\u53ca\u5230\u5355\u72ec\u7684\u6b65\u9aa4\uff0c\u5982\u53c2\u6570\u4f30\u8ba1\u548c\u89e3\u7801\u3002<\/li>\n<li>\u7075\u6d3b\u6027\uff1aRNN\u53ef\u4ee5\u548c\u5176\u4ed6\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\uff08\u5982\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u3001\u81ea\u6ce8\u610f\u529b\u673a\u5236\u7b49\uff09\u65b9\u4fbf\u7684\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u884c\u7a0b\u66f4\u5f3a\u5927\u7684\u7aef\u5230\u7aef\u6a21\u578b\u3002\u800cHMM\u8f83\u96be\u4e0e\u5176\u4ed6\u6a21\u578b\u96c6\u6210\uff0c\u9650\u5236\u4e86\u5176\u5728\u590d\u6742\u4efb\u52a1\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n<li>\u591a\u4efb\u52a1\u5b66\u4e60\uff1aRNN\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u8fdb\u884c\u591a\u4efb\u52a1\u5b66\u4e60\uff0c\u540c\u65f6\u4f18\u5316\u591a\u4e2a\u4efb\u52a1\u7684\u635f\u5931\u51fd\u6570\u3002\u8fd9\u6709\u52a9\u4e8e\u63d0\u5347\u6a21\u578b\u5728\u591a\u4e2a\u4efb\u52a1\u4e0a\u7684\u6cdb\u5316\u80fd\u529b\u3002HMM\u5728\u591a\u4efb\u52a1\u5b66\u4e60\u65b9\u9762\u76f8\u5bf9\u8f83\u5f31\u3002\u56e0\u6b64\uff0c\u5728\u8bb8\u591a\u4efb\u52a1\u4e2d\uff0cRNN\u6bd4HMM\u66f4\u597d\u7528\u3002\u7136\u800c\uff0c\u6839\u636e\u5177\u4f53\u4efb\u52a1\u548c\u6570\u636e\u7c7b\u578b\uff0cHMM\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u4ecd\u7136\u5177\u6709\u4e00\u5b9a\u7684\u4f18\u52bf\uff0c\u6bd4\u5982\u5728\u8ba1\u7b97\u8d44\u6e90\u53d7\u9650\u6216\u8005\u9700\u8981\u5feb\u901f\u89e3\u7801\u7684\u60c5\u51b5\u4e0b\u3002<\/li>\n<\/ul>\n<h3>\u76f8\u5173\u6982\u5ff5<\/h3>\n<h4>\u5e8f\u5217<\/h4>\n<p>RNN\u7684\u8f93\u5165\u662f\u4e00\u4e2a\u5e8f\u5217\uff0c\u4ed6\u7684\u76ee\u6807\u4e5f\u53ef\u4ee5\u662f\u4e00\u4e2a\u5e8f\u5217\u3002\u4e00\u4e2a\u8f93\u5165\u5e8f\u5217\u53ef\u4ee5\u8868\u793a\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">x^1,x^2,...,x^n<\/span>\uff0c\u6bcf\u4e00\u4e2a<span class=\"katex-eq\" data-katex-display=\"false\">x^t<\/span>\u90fd\u662f\u4e00\u4e2a\u771f\u5b9e\u7684\u5411\u91cf\u3002\u540c\u6837\u7684\uff0c\u4e00\u4e2a\u6807\u7b7e\u5e8f\u5217\u4e5f\u53ef\u4ee5\u88ab\u5b9a\u4e49\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">y^1,y^2,...,y^n<\/span>\uff0c\u8bad\u7ec3\u96c6\u901a\u5e38\u662f\u4e00\u4e2a\u6bcf\u6761\u6837\u672c\u5982\uff08\u8f93\u5165\u5e8f\u5217\uff0c\u8f93\u51fa\u5e8f\u5217\uff09\u7684\u6837\u672c\u96c6\uff0c\u5e8f\u5217\u7684\u957f\u5ea6\u53ef\u4ee5\u662f\u6709\u9650\u7684\uff0c\u4e5f\u53ef\u4ee5\u662f\u65e0\u9650\u7684\u3002\u5f53\u4ed6\u6709\u9650\u65f6\uff0c\u5176\u6700\u5927\u7684\u65f6\u95f4\u7d22\u5f15\u4e00\u822c\u88ab\u5b9a\u4e49\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">T<\/span>\u3002<\/p>\n<p>RNN\u4e0d\u4ec5\u9650\u4e8e\u57fa\u4e8e\u65f6\u95f4\u7684\u5e8f\u5217\uff0c\u4e5f\u53ef\u4ee5\u6210\u529f\u5e94\u7528\u4e8e\u975e\u65f6\u5e8f\u5e8f\u5217\u6570\u636e\uff0c\u4f8b\u5982\u9057\u4f20\u6570\u636e\u3002\u7136\u800c\uff0c\u5728RNN\u7684\u8bb8\u591a\u91cd\u8981\u5e94\u7528\u4e2d\uff0c\u5e8f\u5217\u5177\u6709\u663e\u5f0f\u6216\u9690\u5f0f\u7684\u65f6\u95f4\u7279\u5f81\u3002\u4f8b\u5982\uff0c\u5728\u5355\u8bcd\u5e8f\u5217\u201cJohn Coltrane plays the saxophone\u201d\u4e2d\uff0cx(1)=John\uff0cx(2)=Coltrane\u7b49<\/p>\n<h4>\u795e\u7ecf\u7f51\u7edc<\/h4>\n<p>\u795e\u7ecf\u7f51\u7edc\uff08Neural 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